Valverde struck all three goals for the 3-0 Champions League round 16 first-leg win on Wednesday.
The Uruguay international said afterwards: "Incredible. One always dreams of nights like this. I want to thank my teammates who give me the confidence to be in a good mental state; thank the coaching staff and the fans who are always supporting us, even though it has been a difficult season.
"They have always helped and supported us, so I thank them."
Asked if it was the best night of his career, Valverde also said: "Definitely. Especially in terms of goals. I really enjoyed myself today. It had been quite a while since I enjoyed a match this way. I'm happy, I'm joyful, especially for the team's victory.
"For me, it's an honour, as I said yesterday in the press conference. Here we have to treat each other as if we were brothers, defend one another, help each other, and have each other's backs.
"I think that showed. When the team is united, fights for the same goal, and works together, it proves that we can achieve great things."