The former United captain was told he could leave after a meeting with Sir Alex Ferguson in 2005, and Keane said that he was deeply saddened by the news.
"Listen I'm not a robot, I was upset and I did shed a tear out in the car park in my car for about two minutes," Keane told ITV Sport.
"Was it the right time for me to leave? Absolutely not, I could have played there for there for another couple of years in the middle of the park.
"I was hurt, I had no club and I walked out injured [because I was] putting in tackles for the club. My relationship with Ferguson is non-existent."
Keane won seven Premier League titles with the Red Devils.