The 30-year-old started his season-long loan to the Italian side on Monday following several months of speculation over his future.
“If I have one regret, it is the way that I am leaving,” Reina wrote on his official website pepereina25.com.
“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.”
He was reported to be a target for Barcelona at the end of last season but a deal with the Spanish champions never materialised.
In the meantime, Liverpool manager Brendan Rodgers signed Belgian goalkeeper Simon Mignolet from Sunderland.