The big-spending Premier League club have failed to progress from the group stages in the past two seasons but goals from Edin Dzeko, Yaya Toure and Sergio Aguero within 10 second-half minutes raised hopes of an extended run in the competition this season.
It was the Chilean manager's first European game in charge of his new team and he was delighted with the outcome.
"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.
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"Firstly, winning in the Champions League away from home is important, three points is important and we have to continue this. Secondly, it is important to have another clean sheet and also to score three goals is important - this is a good team at Man City."
City dropped points at Stoke City in the Premier League on Saturday as Pellegrini rotated his squad but the former Malaga boss insists that he is not making success in the Champions League a priority.
"We don't have a priority," he stated.
"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 with the same priority.
"The Champions League is very difficult and there are not any easy games and the players know that."