McEvilly admitted Quinn's departure from the Abbey Stadium on Sunday opened the way for his return.
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He said: "He released me and told me in a bad manner which I was really disappointed about."
"I was never going to return when Jimmy Quinn was in charge.
"I don't know what he has [against] the situation with me because he came across as if he rated me as a player but he gave me the cold shoulder.
"But that's football, he's gone and I'm here."
McEvilly said his relationship with U's director George Rolls was important in his decision to return, and said: "George always kept me in touch with the situation that he wanted me to be a Cambridge United player and now I am.
"He wants the club to go forward, and we were one game away from league football and maybe next season we can go up in first place."
United chairman Phil Law admitted it would be ideal for the club to have a manager in place before making further signings.
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"Because he [McEvilly] is such a known entity to us, we felt we had to go and secure his services and not risk him moving to somebody else," he said.
However, Law insisted it was unlikely more players would arrive before the club's next manager was appointed.
"You really want to get the new guy's thoughts on board and him to play a part in the process so I wouldn't have thought so."