City passed a difficult first test by beating a well organised Newcastle United side 2-0 thanks to goals from David Silva and Sergio Aguero on Sunday.
And with three of their next four games pitting them against title rivals Liverpool, Arsenal and Chelsea, Pellegrini was understandably pleased to begin in such fashion.
"I think it's always important to start the season winning, especially at a place like St James' Park," Pellegrini said.
"It was so important for me to have the attitude from the players right from the beginning to the end of the game."
Pellegrini, though, played down suggestions the game had taken on added importance due to the challenging start his side have been handed.
He added: "We're not thinking about the start of the season. We were just thinking about Newcastle. Now we can think about Liverpool.
"All of the teams have to play against all of the other teams home and away. We started with a win and now we can see if we can win the second one."
