Winning European club football's biggest prize is perceived as the 'Holy Grail' for Blues owner Roman Abramovich and he has gone through a string of managers in pursuit of glory.
Jose Mourinho, Avram Grant, Luiz Felipe Scolari, Guus Hiddink and Carlo Ancelotti have all spent time in charge of Chelsea over the past five years without fulfilling Abramovich's ambition.
Israeli coach Grant has come the closest to realising Abramovich's dream following the penalty shoot-out defeat against Manchester United in the 2008 final and now Andre Villas-Boas is charged with the task of trying to satisfy the Russian's desire.
Chelsea start their group campaign at home to Bayer Leverkusen on Tuesday and experienced midfielder Lampard is aware of the importance of winning the Champions League.
"I don't know if it is as cut-and-dried as managers losing their jobs for not winning the Champions League, but I understand where you're coming from - obviously it is something that the owner wants," said Lampard.
"When you've had a lot of domestic success, it's not just the owner but the whole club and the fans, you want that extra step - to win in Europe.
"As a club with what we've achieved in the last six or seven years, it's an obvious thing to say, the one thing that's missing from our cabinet is the Champions League.
"I wouldn't say that's the only reason managers have been sacked, but the pressure is cranked up regardless."
The Blues were knocked out of last season's competition by United at the quarter-final stage while Lampard feels his team can compete with holders Barcelona, who outclassed the Red Devils in the 2011 final.
He added: "Barcelona is the model, they are the outstanding team of recent years, but there's no way that Chelsea are that far behind. We have to believe we can compete with the best.
"We've shown in the past that with our style of play, when we're at our best, we can certainly compete.
"We've been so close in the Champions League and there's been frustration, obviously, as pretty much the same group has stayed for a lot of time. It seems to get tougher every year, because of the quality, particularly in Spain, particularly Barcelona, who have raised the bar.
"I'd like to think we've raised the bar as well. Last season was a disappointment in terms of not winning anything, but I think there's a real freshness about the club."