Rayo won 2-1, with Celta having Marcos Alonso sent off in injury-time. Adri Embarba and Jorge de Frutos struck for Rayo, with Borja Iglesias scoring for the visitors.
Afterwards, Perez said: "I dream that we are three points closer to our goal (of safety). It is true that we are five points away from Europe but we cannot lose focus on the club's main objective.
"I am taking advantage of this euphoria that should be celebrated to use the name of prudence that has given us so much. We must keep our feet on the ground and our focus must be on Thursday in San Sebastian.
"I think we've had a few very good weeks against tough opponents. Against Celta I had no idea that it was going to be a game as complex as when Real Madrid or Barcelona come. We played very well in both areas for 70 minutes. In the last 20 they outplayed us. Today we recovered points that we often deserved."