The veteran defender is leaving Villarreal after six years, though intends to play on next season.
Albiol, 39, addressed fans at the final whistle: "This has been one of the most beautiful stages of my life.
"It has been a perfect day, a nice way to say goodbye to a great club, which has also achieved its objective. From the day I arrived, I was very clear that I was going to give my all, that I was always going to give my best, and with that, I hoped that the fans would be happy with my work and my effort.
"But the truth is that it has been more than I expected, with the Europa League and the Champions League nights."
Doubts after Napoli
Albiol continued: "I had doubts about whether I'd find the same affection at Villarreal that I found in Italy. I came from a club like Napoli that gave me so much, and the people showed me so much affection.
"So I had doubts about finding a similar place, but six years later I can say that I've felt the same.
"I felt very loved and appreciated by the fans and the Villarreal fans. By the Roigs, by everyone at Villarreal and those around them. I would remember the entire journey we took, but the night will always remain a magical one. It's one of the highlights of my career."
Albiol concluded, stating: "In football, apart from the moments you've lived and enjoyed, there are also the people you've met. Receiving the treatment and affection of my teammates is the most important thing; knowing that he was a good person is what I value most."