The defender’s difficult season took another turn for the worse as he was sent off playing for Belgium in midweek.
That came after a series of indifferent performances and mistakes for City, some of which led to him being left on the bench for a game against Leicester last month.
Pellegrini said: “I don’t worry about Vincent because I know him. He knows perfectly in the way he must play.
“I don’t know about the sending off because I didn’t see it but I think he improved a lot with our team in the last game so I don’t worry about him. There are not any problems.”
Kompany was at fault for a goal conceded in the loss at Liverpool on March 1 and his subsequent omission for the visit of Leicester fuelled reports of a dressing-room row with team-mate Fernandinho.
The 28-year-old has been back in the side for the past three games but the scrutiny of his form — and that of several team-mates — has not eased.
City now look unlikely to retain their Premier League crown and it has been claimed the club could be preparing to make major changes to the squad in the summer.
One player under the microscope has been playmaker Samir Nasri, who was left out of the squad to face West Brom altogether last time out after a poor showing in the previous game at Barcelona.
But Pellegrini, speaking at a press conference to preview Monday’s trip to Crystal Palace, played down the reasons for his absence.
The Chilean said: “He is a player of our squad. In this moment we have the complete squad fit, so when you have the complete squad fit you must have two or three names out of the squad list in the next game.
“It can be for different reasons, whether it is physical or tactical, but that can change every week.”
Regarding the summer, Pellegrini was unwilling to discuss what changes might take place at the Etihad Stadium.
The 61-year-old, whose own future has been the subject of speculation, said: “We are just planning how to win at Crystal Palace on Monday. We are not talking about next season — nothing beyond the next game.”
City have again been linked with Liverpool’s Raheem Sterling — a player Pellegrini recently suggested could be worth £100 million (€136.5m) — after the England international’s contract talks at Anfield apparently stalled.
Pellegrini was not interested in discussing the reports.
He said: “The other day I said just one English player but it doesn’t mean we are interested in (that) player. I will not talk about rumours.”
Key midfielder Yaya Toure is likely to return to the side at Selhurst Park after missing the 3-0 defeat of West Brom with an Achilles injury. Pellegrini said: “Yaya played both games for Ivory Coast so he doesn’t have any problems.”
Toure’s future is again in focus after Inter general director Marco Fassone called the midfielder a “dream” target.
The Italian giants are keen to sign the 31-year-old this summer, a player Inter coach Roberto Mancini knows well having guided him from 2010 until 2013 at the Premier League club.
Gazzetta dello Sport claim Inter are prepared to submit an offer of €60m for the Ivory Coast international.
“Who doesn’t dream of having a player like him? Toure would give our midfield line something that we are lacking,” Fassone said. “But his wages and City’s asking price might be a big obstacle.”
Toure has scored seven goals and set up one more in 22 Premier League appearances this term for City.