Pellegrini praise for players
The Toffees went into the clash as the only unbeaten side in the Barclays Premier League but left the Etihad Stadium on the wrong end of a 3-1 scoreline.
It was the same score by which City lost to Munich in the Champions League on Wednesday in a match where they were completely outplayed.
Coming on the back of a league defeat by Aston Villa, it made victory in Saturday's clash very important for Pellegrini's side.
The Chilean said: "I was very pleased for a lot of things. We played the only unbeaten team in the Premier League and a team that plays very well with the ball so it was not an easy game.
"What happened last Wednesday always has a consequence physically and mentally on the team so that's why I am very pleased with the character the team showed."
It was Silva's first start for more than a month after recovering from a thigh injury.
Pellegrini said: "David Silva is a very important player. He has quality, he played very, very well. I wasn't sure if he could play the 90 minutes."
James Milner, another standout performer, also praised the performance of Silva.
The England midfielder told www.mcfc.co.uk: "I think we played well against Aston Villa but ended up losing the game but we didn't perform up to our standards in midweek. It was important to bounce back against Everton, who are a very strong team.
"It was great to have David Silva back, too. He's a top player and any team in the world would miss him.
"There's great movement in this team and everyone is comfortable with the ball. That's what the manager is encouraging us to do - play with freedom in the final quarter of the pitch."
The only major negative for City was the loss of captain Vincent Kompany, who limped off in the first half with what appeared to be a recurrence of a groin injury.