Beatts joined Sheffield United last week and Irvine told the Daily Post: "The emergence of James Vaughan and Victor Anichebe and the fact that they've been doing so well has made it more difficult for James (Beattie).
"If they'd not been playing so well then James would have probably played more football and his confidence would probably have been a bit higher than it is.
"I'm disappointed that things didn't work out for James, I've known James for a very long time and I honestly hoped and thought that things would have worked out for him and I think it's probably best for James to move on at this time.
"I'm talking as someone who knows him well as a person not just as assistant manager of Everton.
"I will contact him and will wish him all the best and continue to follow his career until he finishes in football."