Santa Cruz worked under Pellegrini at Malaga last season and is convinced the Chilean has all the credentials City were looking in for a new manager.
"It is tough to sack Roberto Mancini after his success and I think the fans realise that he deserved to continue but the club keeps moving forward and has high expectations," said Santa Cruz.
"They are obviously chasing the Champions League next and there are few managers in the market that can deliver that.
"Pellegrini deserves the chance to win titles and be successful. He has great qualities when it comes to managing so many stars, a high-profile dressing room.
"The way that he is as a person - relaxed and calm - will make players feel important and part of the City project.
"He is good with squad rotation and a guy who can put everyone on the same ship."
Santa Cruz scored eight goals for a Malaga side that reached the quarter-finals of the Champions League last season.
That success in Europe was one of the factors that attracted City to Pellegrini and Santa Cruz was ideally placed to pass on his knowledge of the English club.
Santa Cruz said: "He did not ask for advice as such but we did speak about the dressing room.
"He is one of those guys who really takes a lot of care when it comes to how healthy the dressing room is in terms of friendship and good guys.
"He was very interested in knowing how the guys are.
"He also had his fears - going into a league he did not know too well - but it won't be hard one bit for him because of the type of person he is."
Santa Cruz joined City from Blackburn in a £17.5m deal in 2009 but, hampered by injury, scored just three goals in 20 games for the club.
He had loan spells back at Blackburn, Real Betis and Malaga before his City contract expired at the end of last season.
Although his City career did not work out, he insists there are no hard feelings.
He said: "I have no regrets but it was tough with my knee - just bad timing at City.
"I wish I did not have it or I could have recovered quicker but no regrets because I worked hard to get fit and be successful with the team.
"They were successful without me which I am very happy about - for Mancini and his people and the players."