Pellegrini has come under increasing pressure with City falling six points behind Chelsea in the chase for the Premier League title and will need to turn around a 2-1 defeat to Barcelona if he is to lead his side to the UEFA Champions League quarter-finals.
The English champions were also knocked out of the FA Cup fourth round by Middlesbrough.
And Inter coach Mancini, who won the league with City in 2012, says there are no excuses for Pellegrini not to collect silverware every season.
"I think Pellegrini was really lucky because he got this team that is a strong team and he has a chance to put in more good players," he told CNN.
"I think City can win a title every year and have a chance - it should and must try to win a title every year.
"It's my opinion that City is the best team in the Premier League. It's in second and six points behind Chelsea but I think it's the best team.
"In the Premier League anything can happen right up to the last game, in the last minute. I think they should think that they have a chance to win the title."
Despite the club's current struggles, Mancini still views City as a team he helped construct.
"Maybe I miss the Premier League because I worked there for three-and-a-half years," he added. "I built the team that is now in second position.
"I think they play with the same players and I am very proud of this."
