Jorge de Frutos scored twice for the 2-1 win, with Rayo now sitting in eighth place.
Perez said afterwards: "Yes (Valladolid was falling apart), but that doesn't sound like a criticism of the rival. Rather, when a team has the three points at home, after what it costs Valladolid or us to score a goal, to get ahead and they come back, well, you get upset.
"You enter into a chaos that is difficult to control. As I said before, I think it has been in our favour and not in their favour, because they had opportunities to do so."
Asked about reaching the top of the table, Perez also said: "No, no. Not at all. Until we get to a stage of the season where there are not seven games left and I can sign this for you, I hope it happens. When there are eight games left I will lie to you, I will tell you that it is not the objective yet.
"I sincerely believe that now is not the time to change the objectives, the first is to stay in the first division. The second is as soon as possible so we can let off steam and have a very nice year."