"I think we really started to believe during the Six Nations when we got into a run of winning games without the internationals. That's something we haven't done in the last two or three years.
"I think that's a great sign of resilience, but we knew we'd have a tough time against Leicester, who are great competitors also."
England star Simon Shaw, named man of the match, admitted the strong start had been crucial to Wasps' victory.
"The first half was the focus for us going into the game, because whenever we have started well against Leicester, we have always ended up winning, though we went to sleep a bit during the second half," he said.
As for Dallaglio, Shaw added: "We didn't want it to be all about the big man. It's about every single man who put it in all season."
Wasps director of rugby Ian McGeechan and Leicester captain Martin Corry also paid tribute to Dallaglio's career.
As a competitor he has been a great man to play against and we have always had some great battles
Leicester captain Martin Corry
McGeechan said: "He is a fantastic example. He plays with emotion, talks with it and leads with it. That rubs off on the players and the coaches that he is involved with.
"I never thought I would see a game when the Wasps fans outnumbered Leicester in the crowd. That was down to Lawrence.
"I think a lot of people made a special effort today to come to this game because of the man."
Corry, a long-time rival, added: "You can just see by all the column inches he has had leading up to this game how highly he is regarded.
"All the plaudits he has had this week have been richly deserved. He has been magnificent for Wasps and England. As a competitor he has been a great man to play against and we have always had some great battles."
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