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The Merseysiders were beaten by Manchester City in a penalty shoot-out at Wembley on Sunday after a 1-1 draw at the end of extra time.
Lallana was one of three Liverpool players to miss a spot-kick, along with Philippe Coutinho and Lucas Leiva.
But the England international believes Jurgen Klopp’s side must use the disappointment of losing as motivation to triumph in the Europa League, in which they face Manchester United in a mouthwatering last-16 tie.
Lallana told the club’s official website: “We are still in the Europa League so hopefully that will give us even more incentive to push on and do well in that competition.
“A few words were said after the game, not many, but the few words was that we have got to push on now in the Europa League.
“We have got a great fixture against Manchester United to look forward to which is massive, the fans will love that, we love that and we have just got to pick ourselves up and go again.”
Despite his shoot-out woe at the weekend, Lallana says he would put himself forward again if the situation ever arose.
He added: “To come so close to winning a trophy and going out on penalties is always tough to take. We won a couple of penalty shoot-outs on the run to this final and you can’t win them all.
“We felt we were in the game throughout normal time and in extra time and going to penalties obviously it can go either way.
“Unfortunately, myself, Phil [Coutinho] and Lucas missed our penalties and we are disappointed because of that.
“I’m sure we would all go again and put our hands up to take another penalty if the opportunity comes, but it’s just disappointing the emotion that is in the dressing room, to come so close to winning a first bit of silverware for the season under the new manager.”