With Brendan Rodgers electing to make new signing Simon Mignolet his first-choice goalkeeper ahead of the coming campaign, the Spaniard signed a temporary deal with the Serie A club this month.
Reina had been widely expected to return to Barcelona ahead of the transfer window, but a proposed switch failed to materialize after Victor Valdes opted to see out the final year of his contract at Camp Nou.
Though Reina admits he would have liked to move to the Catalan club, he insists he was happy to remain at Anfield when that offer did not arrive.
"If I have one regret, it is the way that I am leaving," he wrote in an open letter to Liverpool's supporters.
"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 rumors said it would, as it would be a chance for me to go back home."
The 30-year-old also had kind words for the Merseyside club's loyal support, insisting they are "unique" in world football.
"[Playing for Liverpool] has given me an understanding of what it is like to play for the most wonderful English club," he added.
"I may not have won as many trophies and medals as I would have liked since joining in 2005 but the experiences I have been a part of are as important as any silverware.
"I now understand how supporters can lift a team and inspire them to do special things. I appreciate that there is something unique about Anfield and the atmosphere it creates."
Reina has made 394 appearances for Liverpool since his arrival from Villarreal in 2005, keeping 176 clean sheets in that time.