City fell behind to Ross Barkley's stunning effort after 11 minutes but a Sergio Aguero goal and Edin Dzeko brace turned the game around.
Romelu Lukaku reduced Everton's arrears but City clung on to go top of the table on goal difference, with games to come at home against Aston Villa and West Ham United.
"It is a really, really big step because to play here against Everton is really difficult. You can see that from the scores we have had here in other years," Pellegrini told Sky Sports, before warning against complacency in the remaining matches.
"The worst thing we must do is think that today we finished the Premier League.
"We have to play teams (Aston Villa and West Ham) who are not fighting for anything, they can play without pressure.
"We must try to win our last two games at home, then we will see what happens."
Pellegrini admitted he was not too concerned about performances at this stage of the season, following a nervy end to the match at Goodison Park.
He said: "We won and at this moment the most important thing is to win. Today the pressure was maybe too high to play our best football.
"We played well until 3-2, maybe at that moment the team was a bit nervous.
"We started one goal down and we played good football to recover from that goal. We managed the game, we scored three and had chances."