Ez Abde and Antony had Betis 2-0 ahead before Luca Ranieri pulled one back for the visitors in the first-leg of their Europa Conference League semifinal on Thursday night.
Afterwards, Pellegrini said: "I'm very happy with the performance we played. It was a very complete game. They had very few chances on goal in the first half, except for a header they had, and then they conceded a goal in the second half. We scored two, had more chances, and overall, there's little we can criticise.
"I expect a very balanced match (for the second-leg), just like before this one. They're playing together, with good players. I'm very happy with the team's performance; they barely had any chances.
"We had the personality to go all out from the first minute, and we'll do the same there."
We go to Florence to win
Pellegrini refused to be concerned about the Viola's goal, insisting they'll go to the Stadio Franchi to win.
He continued: "Rather than looking for a more or less wide result, we deserved to win, and we did. There are 180 minutes, and we have to go out there and try to win the game.
"The important thing was to win, and we did. After that, you can win by playing poorly or well, and we did it by playing well. It could have been a bigger score, but that's not a criticism.
"We have a tight score, the first points at home, and we have to have the ability to go after qualification."
Pellegrini concluded: "There are different ways to play, and I'm very happy with what the team did. The best play was one that Pablo Fornals unfortunately shot into the goalkeeper's hands. We created plenty of chances against a team that defends well, and few against a team that attacks a lot."