The Blues boss saw his side concede 3-1 defeat at Stamford Bridge, giving them a record of one win in their last six games.
And Keane, who won seven top-flight titles and a treble at Manchester United, believes that a trait of Chelsea’s managerial history is bad news for Lampard.
Speaking on Sky Sports after the game, the former midfielder said: “The difference between Chelsea and the other clubs is that Chelsea don’t give their players time.
“We’ve had Ole last year, we’ve heard of other managers - these managers are under pressure
“But with Chelsea it’s in their DNA - they don’t give managers time.”
Lampard, though, had a more positive outlook as he pointed back to his own playing days at Stamford Bridge.
He said in the post-match interview: “I sat down with the players and said ‘I’ve had those days and lifted the trophy at the end of the year’.
“I remember getting beaten by Middlesbrough and we were sat in the dressing room pretty demoralised.
“But we bounced back because we had a spirit in the dressing room and quality of player."
This referred to the Blues' 3-0 loss at the Riverside in February in 2006 before going on to win their second league title under Jose Mourinho.
Lampard added: “We’re in a different period of football now but every player is going to have a moment like that.
“Because we’re in a bit of a period, it becomes even harsher for us. The players, myself have to take it on the chin and react.”
When asked if he believed the team had the character to get out of their rough patch, Lampard replied: “Without a doubt.
“We went 16 games unbeaten. What we can control is what we do today, tomorrow and the next day.
“I have belief in the group. When I look at the squad, I know where we’re at because I can see it and I know the work it takes to get to what Man City churned out today.
“It’s normal for a squad to take knocks along the way - it’s a test.”
But fans called for the manager to be sacked as they sit four places worse off from the same time last season.