Despite their success in Europe, the Blues finished sixth in the Premier League as they struggled under the tenure of Andre Villas-Boas.
Lampard insists that Roberto Di Matteo's side must bounce back from that finish and use the success of winning their first major European trophy as a springboard to achieve more.
He told the club's official website: "There is certainly no time to rest on our laurels. Our league form wasn't good enough last season, we weren't consistent enough, and that is something that we have to put right.
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"We need to take the Champions League victory and the FA Cup victory as a platform to more rather than settling for that and not pushing on as a club.
"I am sure with the personnel we have got here, the new signings and the way this club is run, we will keep striving for more."
Lampard also stated that winning trophies matters more to him than personal accolades, and that the Champions League run that led to the final in Munich was the greatest accomplishment by an English team in Europe in recent years, eclipsing Liverpool's penalty win over AC Milan after coming back from 3-0 down at half-time.
He added: "Records are nice and the collective thing is nice as always. The good thing for me was I got the final part of the jigsaw in terms of team trophies and to win the Champions League and the way we did it, for me it was the greatest triumph by an English team in Europe in recent years.
"Liverpool [in 2005] was amazing as a final but our run that we put together was absolutely incredible so I am just delighted with that. Obviously I want to carry on being personally successful but more importantly than that be a successful part of the team.”