In an open letter on his website, the Spain international claims he wasn't informed of the season-long loan to the Serie A side until after the deal was completed.
"If I have one regret, it is the way that I am leaving," said the 30-year-old. "It is only natural that I would be disappointed that the Liverpool management agreed to loan me to Napoli without telling me first.
"I thought that I deserved better than that even though I understand that difficult decisions have to be taken in football.
"A lot has been made about me informing the club that if an offer came in from Barcelona that I would have liked them to consider it. But I had also spoken to the club about the possibility of extending my contract if the offer was not made.
"I told the manager that I wanted to play for Liverpool and that Barcelona would only become an option for me if the opportunity arrived, like the rumours said it would, as it would be a chance for me to go back home.
"My children consider Liverpool to be their home and hopefully their love for the city and also for the club will only grow while we are away," he said.
"I would have liked to have been able to say goodbye in a different way but because of the way the move came about this was not possible.
"Maybe in the near future I can do it properly so that I can show my appreciation to you but all I would ask now is that you keep on inspiring the manager and the players just like you always have done and help Liverpool to become the club that you deserve once again.
"I would like nothing better than to come back at the end of my year away and for Liverpool to be back where they belong."
Reina also thanked the Liverpool fans and believes the club can challenge for major honours this season.
He said: "The supporters deserve the best of times and it would give me so much pleasure to see Liverpool back where they belong, challenging for trophies and getting back into the top four.
"That was where the club was when I first arrived and although I am leaving a different club, one with new owners, a new manager, new players and new challenges, I honestly believe that Liverpool can reach those levels again."