The London side reached the final for the first time in their history this season but suffered a 2-0 defeat to their Premier League rivals in Madrid on Saturday.
Spurs have progressed steadily since Mauricio Pochettino took over at the helm in 2014, but the Argentine coach's future has become the subject of speculation in recent months, while the club are reportedly prepared to offload several players to make way for summer signings.
And Lloris feels his side must use their final disappointment as motivation to continue their improvement next season.
"[Liverpool] set out to win every competition in which they play, and that is not the case with Tottenham," Lloris told reporters.
"We work and try to stick with the [influence] of the board, manager and the club. We look to improve every season and we have shown improvements year after year, so we now cannot throw everything in the bin after a Champions League final defeat.
"It’s been a big step for the club and the only thing we can look to do is come back stronger next season."
He added: "I think it was painful for everyone, to bring Tottenham to a Champions League final will never match the feeling of winning it.
"But [reaching the final] is a very positive thing and we have to build from that in the future to take the club to where it wants to go."
6 - In this season's #UCL, six teams progressed from their post-group stage knockout round ties despite losing the first leg, the most in a single UCL season.— OptaJoe (@OptaJoe) June 2, 2019
Man Utd v PSG
Porto v Roma
Ajax v Real Madrid
Juve v Atlético
Spurs v Ajax
Liverpool v Barcelona
Belief. #UCLrecap pic.twitter.com/8xSZOJrCw9
Tottenham centre-back Jan Vertonghen is unsure if there will be a big turnover in players in the next transfer window, but hopes they can keep their biggest stars together.
"We have a great team," he said. "Hopefully everyone can stay together and we can achieve great things. I hope everyone stays. Will there be an overhaul? I don’t know.
"Today we live with disappointment and we’ll see what happens in the summer."