On Thursday, it was confirmed that the France international had completed a £20m-move to Goodison Park, where he will once again link up with Ronald Koeman following their time together at Southampton.
Schneiderlin only played 11 minutes of Premier League football under Mourinho, but the 27-year-old has said that the Red Devils boss 'was always good to him'.
"No anger at all, Jose has been good to me," Schneiderlin told reporters. "We had some explanation and I can accept the decision he made.
"I have to move forward and I am glad he accepted my decision when I went to see him and said I couldn't see myself spending a year on the bench. I'm a footballer and I don't like to spend one year on the bench."
Schneiderlin is expected to make his Everton debut in Sunday's Premier League clash against Manchester City.