First-half goals from David Silva and Sergio Aguero were followed up by efforts in the second half from Yaya Toure and Samir Nasri as City cruised to an opening game win.
Pellegrini, who replaced Roberto Mancini as manager at the Etihad Stadium over the summer, praised the manner in which City kept up their momentum for the whole game.
"For me, the most important thing was the way my team played for the 90 minutes," Pellegrini told Sky Sports. "We didn't play one way when we were winning 2-0, we tried to play football during 90 minutes.
"We were attacking, defending, an aggressive team with possession of the ball, and we scored four goals but I think we had at least six or seven other chances.
"We didn't concede any goals either and for me it's very important the way my team played the 90 minutes."
Jesus Navas and Fernandinho were handed starting roles and Pellegrini was happy with the contribution of two of City's summer signings.
He added: "Both of them are very important players for us. They're different players.
"Navas always plays wide and he gives a lot of good passes inside the area and Fernandinho works the 90 minutes with the ball and without the ball.
"I'm very happy with both of them for the way they played today."
The win was soured slightly when captain Kompany limped off with 20 minutes to go, which could leave City's defensive resources even more stretched, with Matija Nastasic currently sidelined.
"We'll see during the week with Vincent Kompany exactly what he has," continued Pellegrini.
"We will see what the best thing is that we must do."