The Chilean says he is already focusing on Wednesday night's clash against Aston Villa but was pleased to see his side end their dismal recent record at Goodison Park
The victory moves City top of the table, above Liverpool on goal difference, with just two games of the season left to play.
The Chilean’s side should clinch the league if they win both of their remaining games, against Aston Villa and West Ham, but Pellegrini says the title race is not over yet.
“I think that the worst thing we can do is to think we’ve finished the Premier League now,” he told reporters.
“We have to play games against teams who play with no pressure so it’s important that from tomorrow, we start to think about the game against Aston Villa – we take each game as it comes.
“I think it’s very important to continue in the way we are doing so far – today was the last game away from home and we started this season with four points from the first six away games so I think this team is doing much better in this respect.”
Goals from Sergio Aguero and Edin Dzeko saw City gain all three points against Everton, ending a dismal record at Goodison Park, and Pellegrini admitted it had been a difficult game for his side.
“We’ve won twice in our last ten times here and Everton played really good today – you could clearly see that they wanted to win from the beginning and it was a very tough game for us,” he added.
“We won and that’s the important thing in this moment – the pressure is too high to play our best football but we played well and coped with it.”
“Maybe the team was nervous at 3-2 but we defended well. We started one goal down so it wasn’t easy to recover from that beautiful goal.
“After that we managed the game very well, we scored three and had other chances to score. All of the players played well and all of the team deserve their merits.”