Chelsea will face Barcelona in the semi-finals of the Champions League and remain in the hunt for the Premier League title. But Lampard says talk of a treble just adds unnecessary pressure.
"I hate talk of the treble," he said. "When you talk about it the pressure gets even more so we must keep our heads down and take each game and competition as it comes and if we do that then we will have a chance.
"It will be very difficult to win three but if we can win something then that would be great.
"We are now in a position where we can potentially be very successful this year."
Chelsea had to come from behind for the second time this week to see off Arsene Wenger's side. Having allowed Liverpool to gain a two-goal lead at Stamford Bridge in the Champions League in midweek they were forced to launch a remarkable comeback to eventually draw 4-4 to advance 7-5 on aggregate.
When Walcott put Arsenal in front Chelsea had to dig deep - something Lampard believes they must sort out quickly.
"We started quite slow again and gave them a chance to play and score in the first 20 minutes," he said. "But once we got our game together a little bit, pressed up the pitch and got a bit more physical with them I think we controlled the game and deserved to win it.
"It is a great habit and spirit to keep coming back but it is disappointing to start slow. You put yourself under a bit of pressure which we don't want to keep doing.
"We have got spirit at the moment, are playing well and confident. Once we got back level there was a feeling throughout the team that we would go on and win it.
"We became stronger the longer the game went on. That is one of our strengths, it always has been.
"We are quite powerful but we can also play and create chances. We do the hard work first and then try and get the ball down and play. That is when we are at our best."
Lampard now believes Chelsea must maintain their self-belief to stand any chance of catching Manchester United at the top of league.
Sir Alex Ferguson's side remain four points ahead with a game in hand and Lampard knows all they can do is continue winning and hope the title holders slip up.
"We must keep doing the good things we are doing at the moment – playing together and playing with spirit," said Lampard.
"We must carry that on until the end of the season. We cannot afford to slip in the league.
"We want to keep going and keep putting the pressure on. We want to win all our games because you never know what might happen. It is important we do that and try and keep our form."
Lampard would not be drawn on the future of interim coach Guus Hiddink who insists he will return to his full-time job as Russia's national coach at the end of the season.
Hiddink has lost just one game since he replaced Luiz Felipe Scolari on a temporary basis and there are signs he is really enjoying life at Stamford Bridge.
Unless the Dutchman has a change of heart, the FA Cup final is set to be his last game but Lampard insists the players will have no influence over whether he stays or goes.
"It makes no odds to us," he said. "We have no hold over what happens in the summer.
"That will be decided by the club, by the manager, by everyone else. So as players we are just enjoying the moment and working hard to try and finish the season with success."