Betis took control of their Europa Conference League round 16 playoff, with Antony, Cedric Bakambu and Sergi Altimira settling the first-leg.
Pellegrini said, "The result leaves us with a better place in the standings, but not a done deal. Secondly, I'm happy for the Betis fans who came, we had to try to put on a good show. And thirdly, I'm also happy for the team's performance; we wanted to stick to the idea. We haven't changed our conviction about the footballing line and that's the best way to grow in what you do.
"I'm satisfied. First, because we scored three goals and had several more chances. Second, because we kept a clean sheet and they didn't have many chances. We have a squad that has to try to win the three competitions and go as far as possible. We rotated the team to keep it focused on both LaLiga and the Conference. I'm happy for those who raised their individual level; more than anything, to maintain the collective strength."
He added: "I said at the start of the season that the goal was to qualify for the next round of the Conference. If it wasn't for the play-offs, all the better; but if we were in this round it wasn't a problem. We achieved our goal, but neither I nor anyone else was happy with how we had performed in the Conference.
"Today we played a good game and good football. I'm happy for the Betis fans, who owed it to them. I don't know if it's the biggest away win in Europe. The team had the solidity that was lacking to get the results."