The 29-year-old, who has adopted a pragmatic approach to life under new boss Avram Grant, said: "We all understand what the previous manager did for us and I especially understand what he did for me personally, but you continue playing for Chelsea and that is what I will do."
Lampard, who returned in Sunday's 1-0 win at Bolton after six weeks out with a thigh injury, is concerned that the side are only seventh in the League and warned two wins in the last week does not mean they have turned a corner.
"At a club like Chelsea it is no good getting too excited by one or two results," he said.
"We need to be up there and that is what we have done for the last three seasons.
"It has to be possible to mount a title charge because we are Chelsea. We can't talk about trying to get in the top four, we have to talk about winning titles."