Last week's stunning success at Spurs has handed the ex-England boss a much-need reprieve, however, and Houllier expects his rival boss to survive his time of turmoil.
Houllier said: "That was an absolutely stunning performance. It was phenomenal and one of those games in which the players involved will talk about for the rest of their lives.
"Sometimes when you are playing at home you recover from bad situations and come back, but it's very rare to see that away from home and especially with only ten men.
"That tells me the players are playing for Kevin and I'm pleased to see that. I'm sure he'll turn it around, hopefully starting after our game on Wednesday.
"We have both been criticised this season so I know how he feels. He must feel as though his first name is 'under fire' whereas mine is 'under pressure'. He's a good man and I hope City's results improve."