This season will be Pellegrini's last at City after it was announced Pep Guardiola will take the reins at the Etihad Stadium from 2016-17 onwards.
Fernandinho, a £34million purchase from Shakhtar Donetsk, was Pellegrini's first signing after being handed the City job in 2013.
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The Chilean manager guided the club to League Cup and Premier League glory in his first season, and Fernandinho is hoping he can achieve one domestic success for Pellegrini.
"The first season we won two titles together," Fernandinho told BBC's Football Focus.
"I learnt a lot of things with him so he was like a father for me.
"He introduced me into the team and to play alongside a lot of good players.
"I think he [Pellegrini] did a great job and we've got a great chance to finish with a gold key.
"We have a chance to win the title again and I hope we can do that."