Pellegrini's appointment quickly followed the arrival of former Sevilla midfielder Navas.
"Everything I know about him is positive. Every team he coaches plays well, and everyone in the city will support him," Navas told City's official website.
"He's important because he will help the team and we all know the importance of a good manager and a good person that we trust.
"I think (his teams are good) defensively as well.
"He clearly knows how to take a team, work hard, and get the most out of us."