Garrido, 27, spent three years at City before leaving in 2010 for Lazio.
Norwich's Spanish left-back, on loan from the Rome giants, accepts that Mancini is under pressure.
But Garrido said: "He is a very good manager. I got on well with Mancini. As soon as he arrived at City, he gave me a chance.
"But when the summer transfer window arrived, I had the opportunity to move to Lazio and that was what happened.
"Mancini gets every team he has worked with to the title.
"When you win a title with City after so many years, nobody can tell you anything."