The 33-year-old spent five years at Old Trafford after arriving from Athletic Bilbao in the summer of 2014.
He won the FA Cup, League Cup and Europa League during his time in the red half of Manchester and was voted the club's player of the year in the 2016/2017 season.
Herrera left Manchester United as a free agent in the summer of 2019 and joined Paris Saint Germain but is back at Bilbao on loan from the French champions.
"To leave, it was difficult because six months before, I was expecting that offer for me to stay," a tearful Herrera told United's website.
"It's not the moment to talk bad about anyone, and I am not going to do it.
"But I expected a little bit more from the club. I [won] the Player of the Year, and the club didn't call me that summer to sign a new contract, [like] they did with other players.
"That was painful for me. I think I deserved it, and they didn't do it. After, the conditions changed because I was not happy with that little moment with the club.
"At the end of the third season, [I had won] three titles [and] Player of the Year, and they didn't call me in the summer. I was feeling a bit down."
When the Red Devils eventually tabled an offer, Herrera says it was too late to accept.
"They called me when I had one year left on the contract and the things, they were not right for me," he added.
"They didn't come at the right moment in my opinion, and in my agent's opinion, and in my family's opinion as well."
