Nocioni, who joined the Bulls in 2004 after winning the Olympic gold medal with Argentina in the Athens Games, was guilty of an astonishing miss with the clock ticking in the final minute of a tense contest.
The lead changed hands several times and with 22 seconds left, Nocioni missed an easy layup with Caja Laboral trailing by four points.
The 32-year old, however, remained upbeat about his team's chances to reach the latter stages of the 24-team competition and improving his own form.
Quadruple joy for perfect Spaniards
"We knew it would be a very difficult road game against the defending champions and we should have won it, but a few details decided the outcome," he told the competition's official website (www.euroleague.net).
"It's too early for conclusions because we have just got started and the season is long."
Polish centre Maciej Lampe topped the scoring with 18 points for Caja Laboral, Brad Oleson netted 13 while Fernando San Emeterio, Nemanja Bjelica and Nocioni chipped in with 11 each.
Forwards Georgios Printezis and playmaker Vassilis Spanoulis led Olympiakos with 17 and 16 points respectively.
On Friday, eight-time winners Real Madrid rallied to beat Panathinaikos Athens 85-78 thanks to a superb performance by former Portland Trailblazers point guard Rudy Fernandez.
Real trailed by nine points to Panathinaikos in a battle of former champions but showed all their resilience after the break as Fernandez scored 23 points.
The 27-year old also drew a standing ovation from the home fans when he buried an off-balance fadeaway shot to make the score 81-74 in the final minute and capped his memorable game with a dunk on the buzzer to see off the Greek side.
Centre Sofoklis Schortsanitis, who once played for bitter city foes Olympiakos, led Panathinaikos with 23 points, making all nine shots from the field, but his solo effort was not enough as the supporting cast misfired.
"It's an important win because we managed to beat a good and rebuilt team after losing our initial advantage in the second quarter, said Real coach Pablo Laso.
"We improved our defence when we got back from the locker room and played more attractive basketball after the break," he added.
Elsewhere, Slovenian side Olimpija Ljubljana celebrated their first away Euroleague win in 10 years after upsetting Mapooro Cantu 84-71 while Alba Berlin produced a surprise 92-82 victory at Montepaschi Siena.
CSKA Moscow were stretched in their 75-73 defeat of Lithuania's Lietuvos Rytas Vilnius, 2010 champions Barcelona strolled to a 72-60 win over Germany's Bamberg and Israel's Maccabi Tel Aviv beat Spaniards Unicaja Malaga 85-80.
Zalgiris, CSKA advance into top 16
Maccabi, Zalgiris lose unbeaten records