Goals from Edin Dzeko, Yaya Toure and Sergio Aguero in the space of 10 minutes early in the second half secured a comfortable Group D victory in the Czech Republic.
With champions Bayern Munich the next opponents at the Etihad Stadium in a fortnight, Pellegrini had stressed victory was crucial.
The Chilean said: "I think it is very important to start the Champions League winning away.
"It was not an easy match, against a very good team. Winning 3-0, of course we are very happy.
"In the first half we had three clear chances to score but in the second half we gave a bit more speed to our play and that was very important to create the space against a team that had 10 players behind the ball.
"It was very difficult but we finished what we started in the first half with two or three different things."
City can now look to Sunday's derby against rivals Manchester United at Eastlands in good spirits.
Pellegrini said: "It will give confidence for all the players.
"We have the derby next Sunday and always winning away in the Champions League, scoring three goals, having at least three or four more chances to score and a clean sheet - I think it will give all the players a lot of confidence for the next games."
City are bidding to reach the knockout phase of the competition for the first time after premature exits in each of the past two seasons.
Last season's campaign was particularly frustrating, with the team failing to secure a single win.
They have now already matched last year's points tally and first goalscorer Dzeko, who struck three minutes into the second half, said: "It was very big win for us - it is always important to win the first game.
"In the last two years, we haven't played the way we would have wanted, but this time we did.
"It was a hard first half but then we scored the first goal, and that was important.
"Our quality was better in the second half, but Plzen also played some good stuff in the first half. We had chances and didn't score, but then the goals came.
"The manager told us to keep playing our football and be organised, to concentrate and be aggressive, and that the goals would come. They came."
City, unconvincing in their most recent games, also looked better for the return of captain Vincent Kompany at the back after a three-game absence with a groin injury.
Right-back Pablo Zabaleta said: "It was a good performance by the team.
"We played well, especially in the second half when we came up with some good football.
"We knew it was important to get a win, playing away in the first game of the group, so it was a good start.
"Having Vincent back was good. He is the captain and leader of the team, and it's always good to have him in the team."
Plzen were indebted to saves by Matus Kozacik from Jesus Navas and Dzeko for keeping them in the game in the first half, while Aguero also hit the post.
All that came while City were not at their most fluid and Plzen coach Pavel Vrba conceded the gulf in class between the sides eventually told.
The former Czechoslovakia defender said: "I think the result tells it all. City are one of the top clubs in Europe and I think that showed tonight.
"In the first half we were very lucky to draw 0-0, although we didn't have any luck in front of goal. We played nicely but couldn't score.
"In the second half we made a grave mistake which resulted in the first goal, then City gained too much space and the second goal - which was very nice - was decisive.
"I want to thank my players, they still tried to score even when we were losing but we had no luck finishing."
- Sports & Recreation