Wasps, three-time league champions via the play-offs, failed to reach this season's knockout stages after suffering a crushing 40-26 defeat.
It left the Londoners in fifth place, paying a hefty price for dismal Premiership away form which has seen them record a solitary win on their travels since late September.
But Howard, whose team are now three victories away from completing an unprecedented trophy treble - league title, Heineken Cup and EDF Energy Cup - knows the European final on May 20 will be a whole new ball game.
He said: "This result has no bearing on the Heineken Cup final.
"Two years ago, we beat them at Welford Road in the last round of league games by a bigger margin, and they killed us in the Premiership final two weeks later.
"We scored some nice tries, but they asked us a lot of questions. They also might have had one eye on the Heineken final with Lawrence Dallaglio and Raphael Ibanez being rested.
"They will be fresh by the time of the final. They will be well rested and will have players to add to the team, but we will be match-hardened."
Tigers now host Bristol in the play-offs next Saturday, and Howard added: "They are a good team who I think have the best defensive record in the competition. All the games now are do-or-die."
Wasps rugby director Ian McGeechan pinpointed prop Peter Bracken's sin-binning - Leicester scored two converted tries in his absence - as a critical stage of the contest, claiming: "That effectively was the game lost.
"We did a lot of good things up to half-time, and then had a bad 10 minutes after the break. We missed a kick-off, put ourselves in the corner and could not get out."
Bristol, the Premiership's surprise package this term, finished third despite a 35-13 defeat against table-toppers Gloucester at Ashton Gate.
Head coach Richard Hill said: "We are disappointed we lost the game, but to finish in the top four and into the play-offs is a first for the club. It is a superb achievement from everyone concerned."