But Pellegrini has no doubt the Dutchman can handle the pressure and it will not alter his determination to claim a vital derby at the Etihad Stadium on Sunday.
City, having fallen off the pace in the Premier League title race, are facing a challenge to hold onto a top-four spot and United could apply considerable pressure with victory over their neighbours – a City defeat could see them drop to fifth this weekend if West Ham win at Chelsea on Saturday.
But United’s season has been a turbulent one with Van Gaal having been heavily criticised for both performances and results and finding his future the subject of continual speculation.
Pellegrini said: “I think that Louis van Gaal has a lot of experience. When you are managing big teams, you cannot expect not to receive criticism if you do not win and he has the experience to manage that situation.
“Always – and I am not only talking about Louis van Gaal – when a manager is in a bad moment, you want to support him.
“But I don’t think he has any problems, with the experience he has of managing the big teams during his whole career. He is not maybe in a good moment but he knows how to manage.”
United are in sixth place and suffered the indignity of being knocked out of the Europa League by old adversaries Liverpool on Thursday.
Supporters used to success have become restless but Pellegrini is paying little attention to United’s situation as he expects it to count for little this weekend.
He said: “I don’t think we can take advantage of that. I don’t know what has happened in Manchester United. It’s not my duty (to know) what happens with the fans or Louis van Gaal.
“We will play against a strong team with a lot of history and they will do all they can to win that game, so we must not be trusting in those kind of things.
“We must try to have a good performance to win the game on the pitch.
“When you play a derby it doesn’t matter which positions you are fighting for. The important thing is to win that game because you have to wait for the next season, a lot of months, for the next one. It is always important to have that last win.”