Despite Barcelona running out 2-1 winners, Lionel Messi saw a late penalty saved by Joe Hart, missing an open goal on the rebound to keep City in the tie going into the second leg at the Nou Camp.
And Pellegrini, who saw his side outlcassed in the first-half by two Luis Suarez goals, said the second-half show justified his offensive tactics.
Pellegrini said: “I’m very happy with the way we played. It was the way we must play against Barcelona, we demonstrated that in the second half with the same names.
“Barcelona will always dominate some parts of the game, but with the same players in the second half and losing 2-0 in the second half it was difficult. I think we showed it was the way we must play from the first minute.”
Pellegrini sent out City in a 4-4-2 formation with Edin Dzeko partnering Sergio Aguero up front, and the latter halved the deficit with 21 minutes remaining.
And Pellegrini admitted his team played two different halves, finally finding their flow after the break.
He said: “In the second we did what we talked about before the game, we played well. It’s not easy to play against Barcelona.
“We are going to play at Barcelona and try to do it the way we normally do in Europe. We have a chance.”
The Chilean also conceded he owes a debt of gratitude to Hart for saving Messi’s penalty, which was awarded after the Barca superstar was fouled by Pablo Zabaleta.
“It was a very important save,” Pellegrini added. “It gives us more chance to try and win in Barcelona…3-1 is a very difficult score to try and erase.
“It was a very unnecessary penalty.”
When asked whether he would hand penalty-taking duties to another player in future, Barca boss Luis Enrique said: “No. We know penalties can be missed in this game of ours and he will take the next one.
“Tonight is a night to celebrate. All the first half was fantastic from every player, every person on the pitch.
“I can’t complain about the attitude of the players.”
The two teams meet for the return leg at the Nou Camp on Wednesday, March 18.