Chelsea are seeking a first league title since 2009/10 this term after Mourinho's return to Stamford Bridge, marked on Sunday with a 2-0 defeat of newly-promoted Hull.
England midfielder Lampard was a mainstay of the side in Mourinho's first spell when Chelsea won a first championship in 50 years and retained the title.
Pointing to Chelsea's sixth-placed finish in 2012 and third-placed finish last term, the England midfielder hopes another Premier League title can be won after two seasons of turmoil which have ended in European silverware.
"What we have done in recent years is not stay in the race in the early stages and drop down a few points, then it is hard to get back," Lampard said.
"We are determined to stay in the race this time and stay right up there.
"What matters is what you do out on the pitch. There was certainly a nice buzz (about Mourinho), but this was his first game and things will settle.
"What we can't do is settle ourselves, we have to keep pushing."
Lampard, whose pre-season action was limited by an Achilles problem, had an eventful outing.
His early penalty was saved by Allan McGregor before he beat the Scotland goalkeeper with a vicious free-kick for Chelsea's second, after Oscar had given the hosts the lead.
Mourinho believes no team will be able to cope with his Chelsea side if they can sustain the level of performance they showed in the opening half an hour.
"Everything was there," he told Chelsea TV.
"If we play one game for 90 minutes the same way we played the first 30, we destroy any team that comes here. (But) we couldn't do it."