The left-back has come under scrutiny after struggling for form since recovering from his broken leg last season.
Mourinho publicly lambasted the defender, questioning his focus and commitment.
Luke Shaw's next club: Where could the left-back go next?
Mon, April 3, 2017
Express Sport brings you the Premier League clubs tipped to land Manchester United outcast Luke Shaw. Odds provided by Betfair
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Man City – 33/1
Then following Shaw's display against Everton on Tuesday, Mourinho claimed he was the reason for his improvement.
And former Arsenal defender Keown feels Mourinho's treatment of Shaw has been "poor management".
Manchester United's Luke Shaw arrives before the match
He told BBC Sport: "Why not believe in Luke Shaw? What about saying he played well, what about saying he came on and led to the equaliser against Everton?
"Saying he was only doing well because of what Mourinho was telling him to do is poor management.
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"He should apologise sometimes for what he has said."