The Chilean saw his new charges ease to a 3-0 win at Viktoria Plzen thanks to three goals in 10 minutes from Edin Dzeko, Yaya Toure and Sergio Aguero.
Pellegrini felt his side stepped up a gear in the second half which saw them claim their first UEFA Champions League win since late 2011.
"The first half we had a good match, we have three or four clear chances to score but I think the second half we played really well," he told Sky Sports.
"We made some movements so we could create space which is needed, as with 10 players behind the ball it is very difficult to try and score so we had to get more from our game and we got three goals."
Pellegrini insists that City are not prioritising the Champions League ahead of the Premier League, despite resting a number of players last weekend in the draw at Stoke City.
"We don't have a priority," he insisted.
"We know that Manchester City didn't play well in the Champions League last season, but the Premier League is also very important for us, we will try to continue in both sides with the same priority.
"The Champions League is a very difficult, and there are not any easy games and the players know that."
The City chief feels the club can take a number of positives from the win in Plzen.
"Firstly winning in the Champions League away from home is important, three points is important and we have to continue this," he said.
"Second it is important to have another clean sheet and also to score three goals is important, this is a good team at Man City."
Captain Vincent Kompany made his first appearance of the season and Pellegrini confirmed that he is now fully fit ahead of this weekend's Manchester derby.
"Vincent has worked very well in last few days, I had some doubt in last the last 10 minutes to change him but I saw he was playing without fear so he will arrive without a problem," he concluded.