Kaka out of Valladolid clash
Kaka has come under fire in the Spanish media for some disappointing performances since his move from AC Milan and will miss Sunday's match at struggling Real Valladolid after picking up a muscle problem in training.
"He is adapting to a new league and has all my support," Pellegrini told a news conference.
"He has provided a good number of goals and assists," added the Chilean. "He is an example as both a person and a professional, even if we know he can still give more."
Pellegrini defended the team's tactics following their shock Champions League exit on Wednesday at the hands of French side Olympique Lyon, the sixth straight season Real have failed to reach the quarter-finals of Europe's elite club competition.
"We are on the right path, the team is playing well and we are playing in a way that the fans like," he said.
"At Real Madrid you go from glory to despair very quickly. I have absolute conviction about what I am doing."
League leaders Real are level on 62 points with champions Barcelona, who host third-placed Valencia on Sunday.