A day after clinching the Premier League title, Pep Guardiola's under-strength City side defeated Chelsea 1-0 on Sunday and celebrated with an emotional trophy presentation, while Chelsea were left to lament their mid-table position.
"Man City have not won three (Premier League titles) in a row through trotting out at half intensity and just going through the week. They work and work and work," Lampard said.
"Pep's work in terms of changing the team to keep moving it forward, everyone involved, gets to this level where you're lifting trophies. There's a load of work.
"The players have to understand that every personal responsibility, if you want to get there and be there like (Erling) Haaland and (Kevin) De Bruyne etc, today, (means) 'I need to put in the work that those boys have put in.'
"It's a nice symbol for them (Chelsea's players) in a way... if you know what I mean by nice. It's something they need to strive towards but it doesn't come easy, that would be my advice."
Lampard, who won three Premier League titles among 11 major trophies as a midfielder at Chelsea and is the club's all-time leading scorer, was appointed as interim manager in early April after the sacking of Graham Potter.
But he was not able to right the ship and, when asked on Sunday if he would be willing to stay as a coach, he said: "No. A new manager will come in and bring his own coaches, I'm sure."
British media have reported that Chelsea have reached an agreement to appoint former Tottenham Hotspur and Paris St Germain boss Mauricio Pochettino (51) as their new manager.
Asked whether or not Chelsea will be able to rediscover the glory of past years, Lampard said it was tough to tell what the struggling club's future might hold.
"It's in their hands," he added. "I can't say. I got asked how long will it take, we don't know. It's down to the players themselves that we have. For the club it will be down to the direction we take it forward, for the new coach.
"This Premier League is getting tougher. We've felt that this year ... there are things we need to improve for next year. To get to where Manchester City are, a lot of things have to align so there's a lot of work to be done.
"There's clearly talent in the squad, a lot of young talent in the squad, maybe a lack of stability in the squad, maybe a bit of imbalance in the squad.
"Those things are maybe club issues and every player has to really get to work to see if they can get us back to where we want to be."
