Pellegrini took over at the Etihad Stadium following the dismissal of Roberto Mancini in May and Begiristain feels that the Chilean's presence has had a positive impact on the mood in a dressing room.
"The most important thing was to change the environment of Carrington (City's training ground)," Begiristain said.
"Now the atmosphere is very good. There’s a lot of confidence."
The former Barcelona director of football was speaking after the UEFA Champions League group stage draw on Thursday, which saw City pitted against holders Bayern Munich, CSKA Moscow and Viktoria Plzen.
City failed to progress beyond the group stage in each of their last two Champions League campaigns under Mancini, but Begiristain is confident Pellegrini can guide them into the knock-out rounds this time around.
"This kind of manager gives a lot of confidence to the players and we are recovering the confidence of the players who were really down last season," Begiristain added.
"You can talk about his style of play, his experience in the Champions League and his background is really good. There’s more width and the full-backs play more forward.
"We are happy with the manager’s tactics. The manager has a lot of experience in the Champions League. We are now in the right situation to think that we will do a very good Champions League.
"We want the expectation. It means people think we have a very good squad and opponents think we are stronger than last season."
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