Newcastle released a statement last week confirming an end to the three-year association with the Spaniard after the two parties could not agree terms on a new deal.
Benitez, in an open letter to fans of the Tyneside club, revealed that he was wanted to continue for a longer term but the club’s board thought otherwise.
"I wanted to stay, but I didn't just want to sign an extended contract, I wanted to be part of a project," Benitez said.
"Unfortunately, it became increasingly clear to me that those at the top of the club did not share the same vision.
"I'm very sad about that, but I do not regret for one moment my decision to come to Tyneside and I'm very proud about what we achieved together.
"I will always have you in my heart. Best of luck for the future."
Benitez joined a relegation-threatened Newcastle United side in March 2016 but was powerless in preventing them from dropping down to the Championship.
The Champions League winner however got Newcastle United promoted back to the Premier League at the first time of asking and kept them in the top flight for two straight seasons despite operating on a strict budget.
Newcastle United finished 10th and 13th in Benitez’s two seasons with them in the Premier League but the former Real Madrid, Chelsea and Liverpool manager left the club following the expiration of his contract on Sunday.
Chinese Super League side Dalian Yifang have been touted as Benitez’s next possible destination.
