Pellegrini watched his side claim their first away Premier League victory this season with a 3-1 success at West Ham thank to two goals from the excellent Sergio Aguero, who then set up David Silva for the late third after Ricardo Vaz Te had pulled one back.
City have now climbed to fourth in the Premier League table ahead of their next domestic test - a tough trip to title rivals Chelsea next Sunday.
After 3-2 defeats at Cardiff and Aston Villa in their first three away games this season, City boss Pellegrini said: "Winning the game was most important thing for us.
"The team played very well, we scored three goals, the best player for West Ham was their goalkeeper - he made four or five important saves.
"I spoke with the players before the game. We lost two games away 3-2... to score two away is a good average. Today we scored three again, so we will continue trying to be an offensive team.
"Having players of the quality of Silva, Aguero, Nasri, Dzeko, I think this team must always play on the attack.
"It is never a problem to have good players on the bench. It's more important when you don't have players who can change a result.
"That's why for us it's very important to have players of good quality because we have a lot of games to play this year. The quality of players is what makes the difference.
"I said I think we must keep all the (good) things we have done in the other games but concentrate more on the defending, that is what we have done today.
"Before we started the game, we knew Chelsea and Arsenal had won their games so we wanted to only be three points behind the leaders.
"We will try in the next game away at Chelsea to recover the points we lost at the beginning of the Premier League.
"It's not a normal, the games we lost against Cardiff and Aston Villa - but football is like that and today we played well."