The Ivorian has not been able to find his best form in recent weeks and came under fire for his performance during the club's Champions League defeat against Bayern Munich on Wednesday evening.
In May, Toure was involved in a row with the club's owners, after claiming that they had shown him a lack of respect on his birthday.
A month later, while he was at the World Cup, he learned of the death of his brother Ibrahim Toure, and Pellegrini believes that his personal problems have affected him.
"We must support him because he is a very important player," BBC Sport quotes him as saying. "Maybe he had a lot of personal problems with his brother.
"There are a lot of human things and maybe that is why he is not in his best performance at the moment.
"I think as a team, as a coach, as a club we must support him because he is a very important player, he makes a difference and I'm sure he will return to his best. But he is always being criticised."
Toure scored 20 goals in the Premier League last season to help City win the title.