The 23-year-old has endured a troubled start to life in the Premier League since making a £32m move from Porto in the summer.
The situation evokes memories of Martin Demichelis for Pellegrini, who staunchly defended him after the Argentine also endured a much-scrutinised introduction to English football.
"The same thing happened with Martin Demichelis last year. Remember all the criticism for him after he just arrived in the Premier League," the Chilean told the Daily Mail.
"I think Eliaquim Mangala is a young player and he has a lot of experience. I am sure we bought the centre-back that we need in him."
City, who sit six points adrift of Premier League leaders Chelsea, host bitter rivals Manchester United at the Etihad Stadium on Sunday.