The 1-0 victory came via Johnny Cardoso's goal and sees Betis reach the competition's playoffs in February.
Pellegrini said afterwards: "I'm very happy because we won 1-0. They didn't score against us and they had been scoring against us in the last few games.
"The team spent the whole 90 minutes trying to make the difference. We had chances but we didn't take advantage of them. We didn't have enough intensity and desire, but we lacked a lot of composure and precision.
"We have direct football players who run and want to get to the opponent's area quickly. It would have been important to score the second goal to play more calmly, but the attention was maintained from the first minute to the last.
"The objective was to qualify and we achieved it."