The Briton leapt 8.08m to finish some way off behind China's Jinzhe Li (8.34m) and Russia's Aleksandr Menkov (8.31m).
"Not a fantastic performance," Rutherford tweeted. "Gutted I missed that 4th round. What could have been!"
"I go to every competition to win it," he said in an inteview afterward. "That's why I'm disappointed to finish third today.
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"Going forward, by the time Moscow comes around I expect to be in very good shape and hopefully able to jump a lot further than last year," Rutherford added.
He did, however, finish ahead of former Olympic champions Irving Saladino and Dwight Phillips.
Team GB's Olympic bronze medallist Robbie Grabarz was fifth in the men's high jump after equalling his season's best of 2.24m.
Olympic 100 metres champion Shelly-Ann Fraser-Pryce eased to victory while world champion Carmelita Jeter was stretchered off the track after finishing third.
As low clouds settled around the stadium for the evening meet, the Jamaican sprinter pulled away from her American rival to clock 10.93 seconds, the fastest time of the year.
"I just came out to execute a good race, and I think I did that," Fraser-Pryce said. "I'm just looking forward to the rest of the season.
"I pray to God that if I can continue to stay healthy, that is key at this moment because it's a long season."
Jeter, who needed treatment for a leg injury, told stadium officials that it was too early to know the extent of her injury.
In the men's 400 metres, London gold medallist Kirani James eased away from American rival Lashawn Merritt down the home straight.
"It was good, I had Lashawn in front of me. And so he really set the pace and it kind of prepared me to put on a good performance," said the Grenadian sprinter.
It was the first time the two rivals have met since Merritt was forced to pull out last year's London Olympics.
"It's my first 400, my opener and I've got a lot more training to put in. I've been training hard, came out and ran a healthy race," said Merritt. "Is he unbeatable? Not at all. Everybody's beatable. Next race I'll come more prepared and we'll go at it again."
Chinese sprint hope Zhang Peimeng broke the national 200 metres record just weeks after he ran China's fastest 100 metres, but failed to trouble the leaders as Olympic bronze medalist Warren Weir pipped American rival Justin Gatlin.
"It's not a surprise for me to break the national record since I have already proved myself in the 100. I feel I still have room to improve and I can do better next time," Zhang said.
In the 110 metre hurdles, London silver medallist Jason Richardson won in 13.23 seconds after his fellow-American Aries Merritt sustained an injury in the warm-up.
"I felt a cramp in my hamstring and I didn't want to risk it. I didn't want to pull my hamstring and be done for the season," said Olympic champion and world record holder Merritt.
Richardson said he was concentrating on the Moscow world championships in August.
"I'm thinking about Moscow every day to defend my world championship title. I just need to make sure I peak in August," he said.
In the absence of high hurdler Liu Xiang, a number of local athletes put in strong performances, with Li Jinzhe leading the field in the long jump and Xie Wenjun coming third in the 110 metre hurdles.
Ethiopian Genzebe Dibaba outpaced Olympic champion and compatriot Meseret Defar in the women's 5,000 metres. Defar snatched Olympic gold in London from Genzebe's sister Tirunesh.
Russian world record holder Yelena Isinbayeva won the women's pole vault with a mark of 4.70, before falling short on two attempts to reach 4.85.
"There's no point in just jumping 10 centimetres higher," she said. "I was confident if there was no pain then I could jump higher than 4.85 and maybe 4.90."
Men's 200m
1.Warren Weir (Jamaica) 20.18
2. Justin Gatlin (U.S.) 20.21
3. Jason Young (Jamaica) 20.22
4. Zhang Peimeng (China) 20.47
5. Churandy Martina (Netherlands) 20.59
6. Darvis Patton (U.S.) 20.61
7. Xie Zhenye (China) 20.63
8. Wallace Spearmon (U.S.) 1:20.88
Men's 400m
1. Kirani James (Grenada) 44.02
2. LaShawn Merritt (U.S.) 44.60
3. Luguelin Santos (Dominican Republic) 45.11
4. Jonathan Borlee (Belgium) 45.57
5. Lalonde Gordon (Trinidad and Tobago) 46.39
6. Zhang Huadong (China) 47.77
. Pavel Maslak (Czech Republic) DSQ
. Conrad Williams (Britain) DSQ
Men's 1500m
1. Asbel Kiprop (Kenya) 3:32.39
2. Gebremedhen Gebremariam (Ethiopia) 3:32.43
3. Collins Cheboi (Kenya) 3:32.96
4. Abdalaati Iguider (Morocco) 3:33.29
5. Bethwell Birgen (Kenya) 3:33.67
6. Silas Kiplagat (Kenya) 3:33.85
7. James Kiplagat Magut (Kenya) 3:35.29
8. Teshome Dirirsa (Ethiopia) 3:35.47
Men's 110m Hurdles
1. Jason Richardson (U.S.) 13.23
2. Ryan Wilson (U.S.) 13.25
3. Xie Wenjun (China) 13.28
4. David Oliver (U.S.) 13.35
5. Jeff Porter (U.S.) 13.45
6. Sergey Shubenkov (Russia) 13.52
7. Shi Dongpeng (China) 13.64
8. Lehann Fourie (South Africa) 13.82
Men's 3000m Steeplechase
1. Conseslus Kipruto (Kenya) 8:01.16
2. Paul Kipsiele Koech (Kenya) 8:02.63
3. Hillary Kipsang Yego (Kenya) 8:03.57
4. Abel Kiprop Mutai (Kenya) 8:08.83
5. Gilbert Kiplangat Kirui (Kenya) 8:09.50
6. Jairus Kipchoge Birech (Kenya) 8:10.27
7. Brimin Kiprop Kipruto (Kenya) 8:14.97
8. Bernard Mbugua Nganga (Kenya) 8:20.69
Men's High Jump
1. Mutaz Essa Barshim (Qatar) 2.33
2. Bohdan Bondarenko (Ukraine) 2.33
3. Zhang Guowei (China) 2.27
4. Michael Mason (Canada) 2.24
5. Robert Grabarz (Britain) 2.24
6. Aleksandr Shustov (Russia) 2.24
7. Trevor Barry (Bahamas) 2.24
8. Sergey Mudrov (Russia) 2.20
Men's Long Jump
1. Li Jinzhe (China) 8.34
2. Aleksandr Menkov (Russia) 8.31
3. Greg Rutherford (Britain) 8.08
4. Su Xiongfeng (China) 8.00
5. Ngonidzashe Makusha (Zimbabwe) 7.96
6. Ignisious Gaisah (Ghana) 7.95
7. Godfrey Khotso Mokoena (South Africa) 7.74
8. Irving Jahir Saladino Aranda (Panama) 7.72
Men's Discus Throw
1. Piotr Malachowski (Poland) 67.34
2. Gerd Kanter (Estonia) 63.14
3. Robert Urbanek (Poland) 62.85
4. Erik Cadee (Netherlands) 62.40
5. Yennifer Frank Casanas (Spain) 62.39
6. Vikas Gowda (India) 61.97
7. Martin Maric (Croatia) 60.73
8. Rutger Smith (Netherlands) 60.12
Men's Javelin Throw
1. Tero Pitkaemaeki (Finland) 87.60
2. Vitezslav Vesely (Czech Republic) 86.67
3. Dmitri Tarabin (Russia) 85.36
4. Ari Mannio (Finland) 83.43
5. Zhao Qinggang (China) 81.18
6. Keshorn Walcott (Trinidad and Tobago) 79.02
7. Julius Yego (Kenya) 78.23
8. Stuart Farquhar (New Zealand) 76.36
Women's 100m
1. Shelly-Ann Fraser-Pryce (Jamaica) 10.93
2. Blessing Okagbare (Nigeria) 11.00
3. Carmelita Jeter (U.S.) 11.08
4. Samantha Henry-Robinson (Jamaica) 11.23
5. Sheri-Ann Brooks (Jamaica) 11.27
6. Aleen Bailey (Jamaica) 11.30
7. Ruddy Zang Milama (Gabon) 11.36
8. Jeneba Tarmoh (U.S.) 11.42
Women's 800m
1. Francine Niyonsaba (Burundi) 2:00.33
2. Janeth Jepkosgei Busienei (Kenya) 2:01.28
3. Malika Akkaoui (Morocco) 2:01.49
4. Winny Chebet (Kenya) 2:01.54
5. Marina Arzamasova (Belarus) 2:02.44
6. Wang Chunyu (China) 2:02.81
7. Tatyana Markelova (Russia) 2:02.92
8. Zhao Jing (China) 2:02.94
Women's 5000m
1. Genzebe Dibaba (Ethiopia) 14:45.92
2. Meseret Defar (Ethiopia) 14:47.76
3. Viola Jelagat Kibiwot (Kenya) 14:48.29
4. Mercy Cherono (Kenya) 14:49.84
5. Mary Wangari Mureithi (Kenya) 14:49.92
6. Buze Diriba Kejela (Ethiopia) 14:50.24
7. Irine Chepet Cheptai (Kenya) 14:50.99
8. Gelete Burka (Ethiopia) 14:59.05
Women's 400m Hurdles
1. Zuzana Hejnova (Czech Republic) 53.79
2. Angela Morosanu (Romania) 53.85
3. Yadisleidis Pedroso (Italy) 54.54
4. Dalilah Muhammad (U.S.) 54.74
5. Kaliese Spencer (Jamaica) 54.91
6. Lashinda Demus (U.S.) 55.12
7. Muizat Ajoke Odumosu (Nigeria) 55.94
8. Tiffany Williams (U.S.) 56.05
Women's Pole Vault
1. Elena Isinbaeva (Russia) 4.70
2. Mary Saxer (U.S.) 4.60
3. Silke Spiegelburg (Germany) 4.55
4. Li Ling (China) 4.50
5. Lacy Janson (U.S.) 4.40
6. Anastasia Savchenko (Russia) 4.40
7. Angelica Bengtsson (Sweden) 4.40
8. Becky Holliday (U.S.) 4.15
8=. Natalya Kushch-Mazuryk (Ukraine) 4.15
8=. Katy Viuf (U.S.) 4.15
Women's Triple Jump
1. Caterine Ibargueen (Colombia) 14.69
2. Olha Saladuha (Ukraine) 14.43
3. Irina Gumenyuk (Russia) 14.02
4. Xie Limei (China) 13.99
5. Kimberly Williams (Jamaica) 13.99
6. Niki Panetta (Greece) 13.81
7. Dana Veldakova (Slovakia) 13.76
8. Keila Costa (Brazil) 13.63
Women's Shot Put
1. Christina Schwanitz (Germany) 20.20
2. Gong Lijiao (China) 19.73
3. Michelle Carter (U.S.) 18.83
4. Liu Xiangrong (China) 18.11
5. Anca Heltne (Romania) 18.02
6. Josephine Terlecki (Germany) 17.97
7. Jeneva Mccall (U.S.) 17.83
8. Anita Marton (Hungary) 17.23
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