"We're in another final, we beat a very good team," Saracens number eight Billy Vunipola told the club's website. "I think our focus is enjoy tonight and then we've got a big week ahead of us next week."
Saracens, who were crowned European champions last weekend, kept their double hopes alive after a dominant first-half performance against Leicester put them 31-0 up at the break.
They took the lead when flanker Will Fraser finished under the posts after seven minutes before a double from winger Chris Wyles and another try from winger Chris Ashton left the Tigers with a mountain to climb.
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Leicester reduced the deficit with early second-half tries from winger Telusa Veainu and lock Dom Barrow but Ashton's second sent twice Premiership champions Saracens into the final at Twickenham on May 28.
"The team have been outstanding all year," Ashton said. "Confidence is not something that we're lacking, but it all go down to next week now.
"If we lose next weekend, we'll be finishing with a very sour taste in our mouths."
Leicester centre Manu Tuilagi and Saracens flyhalf Owen Farrell limped off the field due to injuries and could be doubtful for England's tour of Australia which starts next month.
Exeter reached their first final after seeing off Wasps in a gripping match at Sandy Park.
The hosts started strongly with two Gareth Steenson penalties and went in 20-14 at the break after Ian Whitten's touchdown and a penalty try cancelled out tries from Wasps pair Carlo Festuccia and Dan Robson.
Dave Ewers gave Chiefs a 10-point lead when he burst over the line early in the second half and while Wasps closed the gap with two penalties, a penalty try awarded to the home side at the death sealed their place in the final.
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