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."
With important matches to come against Aston Villa on Wednesday and at defending champions Manchester United next Monday, Lampard hopes Chelsea can at least be in title contention for longer this term.
"The Premier League is very difficult these days, the games come thick and fast and consistency is difficult," he added.
"What the manager did last time he was here was to keep us on the ball so we won week in, week out and that's what we have to do again.
"What matters now is Aston Villa come on Wednesday after beating Arsenal with a very quick and young team, so we can't rest on our laurels. We have to keep kicking on."
Chelsea, too, have a young team, with Lampard, John Terry, Petr Cech, Ashley Cole and Michael Essien surviving members from Mourinho's first spell in charge, which came to an abrupt end in September 2007.
"The young people, they need the older generation to be amongst them," said Mourinho, whose team selection was made with experience in mind.
"Playing or not playing, being in the line-up or not, we need these four, five players that we have - and they're doing fantastic work - to support the other kids."
Lampard enjoyed the atmosphere on Mourinho's homecoming and is pleased to be reunited with his former boss.
"There is a lovely buzz around the place," Lampard added.
"I am happy myself to be here and I was very excited in the morning to get going again and the whole stadium was buzzing with the manager returning.
"You can see what it means to him. All it needs now is for us to go and perform consistently and keep getting results."
It was a tough baptism for Hull, who improved as the match wore on.
Manager Steve Bruce is optimistic his players will rise to the challenge in the Premier League.
"It's a wake-up call to us, if we ever needed it, that we've arrived on the big stage," Bruce said.
"Some will shrink with it and some will grow into it and make a fist of it.
"I'm convinced the vast majority of them will make a fist of it and be successful."
Next Hull play Norwich at home, with captain Robert Koren demanding a stronger display.
"We need to learn quickly from this defeat," Koren said.
"In the second half we showed if we're not scared and we have belief, we can play at this level.
"We need to learn from this and we need to be up for it from the first minute in the next game."