The result sees Betis sitting in fifth place, six points outside the top four and the Champions League slots.
Pellegrini said, "I rate it as a very important victory because we had a very poor first half, perhaps with overconfidence, even though we had talked about it, that even if Valladolid was in a bad moment, if you lower the intensity any team will complicate things for you.
"In the second half we completely turned things around and ended with a very important victory that allows us to be in the Champions League places at this moment and reduce the goal difference. I hope we can maintain this form until the end of the season."
On the race for the top four, he also stated: "In football, as long as the math works out, you have to believe you can do it. To do that, you can't make mistakes.
"Athletic Club is six points ahead of us, plus goal difference. But we're focused on trying to beat the next team. Today it was Valladolid, now we're focusing on the Conference and then Espanyol.
"We're taking it with the calmness it requires, with enthusiasm and the ambition we've always tried to instill in this club."