The Aviva Premiership final win could be seen as revenge for Mark McCall's side after they lost to the Tigers in last year's final and Burger told ESPN that he would have been heartbroken to lose again.
"It was an amazing game, Leicester came at us the whole time but we were happy. I can't lie it (last year) did go through my head, it would have been heartbreaking if there was a repeat of last year," he said.
"You learn from your mistakes and last year we learned you can't give a good team like Leicester one minute."
Saracens hooker Schalk Brits was awarded the official man of the match accolade and he dedicated the victory to the supporters of the club.
He said: "We're doing it for everyone that has been supporting us for years, all the coaching staff and players, it is two years hard work for everybody.
"After last year revenge feels very sweet. The Leicester boys had an amazing second half. That is what we expected. They are an amazing side and a never say die attitude."
Owen Farrell kicked five penalty goals during the match and admitted he was delighted to win the showpiece final.
"I'm lost for words, to come here at this special place and do that, it is unbelievable," he said.
"I'd like to say I did them as any other kick but it is not the same here."
Saracens' director of rugby McCall hailed the character of his players but insisted they must now build on this success.
"For the first hour of the match we were in control, I think in some ways it was fitting that it ended in that way to defend three or four minutes showed our character and how much they work for each other," he said.
"We want to be here every year and we want to be like Leicester because they are a great club."
Andy Farrell, Saracens' coach and father of Owen, praised the hard work the squad put in to achieve such success and also acknowledged the work of the board.
He said: "Obviously I'm proud as a father but even more so as a coach. These boys have worked unbelievably hard over two years.
"There are a lot of board members who have been here and it has been a long time coming, they put their heart and soul into this club."
Leicester coach Richard Cockerill admitted that Saracens were the deserved winners of the final.
"We had our chances to win it but they played well - we found it hard to break them down and they scored the only try so it is disappointing," he told ESPN.
"I think they hit us hard and opened holes in us. You have to give them credit, they probably deserved to win today," he said.
Despite ending the season empty-handed Cockerill refused to label the campaign a failure.
"It is disappointing but it is not a failure. We were very close in Europe and we lost by four today and we could have won it. Saracens take the spoils and you can't argue with that.
"We have lots of young players and guys coming through, we have had bad injuries but still done really well," he added.
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