Kompany's form this season has been the subject of scrutiny with TV pundit Paul Scholes, the former Manchester United player, cutting in his analysis during Tuesday's Champions League loss to Barcelona.
Centre-back Kompany was criticised for failing to clear a cross that led to Luis Suarez's opener in the 2-1 defeat and being caught out again for the Uruguayan's second at the Etihad Stadium.
Kompany also came under fire from other analysts for his role in Arsenal's first goal in a 2-0 Barclays Premier League loss last month.
But Pellegrini said: "Vincent is an experienced player with a strong character
He must receive the criticism that everyone receives when our team doesn't have the performance that everyone hopes for.
"I think it's not a problem for him, I am sure that he will have a strong reaction."
Asked if the Belgian could still be regarded as one of Europe's best defenders, Pellegrini said: "I think he is a great player."
Pellegrini, speaking at a press conference to preview Sunday's trip to Liverpool, added that he would keep his own thoughts about the individual performances of his players in-house.
The Chilean said that he and the whole team had to take collective responsibility for the result.
He said: aid: "I don't defend the performance of the team - not just Kompany.
"We played moments of the game, the first 25 minutes and all the second half, without any problem.
"But I think the parts of the game that decided the score were because of poor performance from me and from the team - everyone, not just individuals or the skills of just one player.
"I always talk with the players about their level in private
I don't analyse what they do to the media."
Kompany, 28, has been a highly influential figure at City in recent years, providing the bedrock for their title successes of 2012 and 2014.
It has also been suggested that his lack of a regular partner this season, with Pellegrini alternating between Eliaquim Mangala and Martin Demichelis, might have been disruptive.
Pellegrini does not believe that to be the case, instead pointing out that Kompany did miss most of December with hamstring problems.
He said: "I don't think so
We work every day during the training sessions with different names
The performance of the players doesn't depend on who they play with.
"He is also coming back from a long injury and it's not easy for a player coming back to give 100 per cent."
Source : PA
Source: PA