United are currently sixth in the Premier League, but stand a chance of winning the Europa League.
Keane, however, thinks their performance domestically has not been good enough, after spending big on players last summer.
“They are now sixth in the league, I think they are 19 points behind Chelsea. The manager and the players should be embarrassed by that,” he told ITV.
“For a club like Man United be as far behind Chelsea as they are, it’s an embarrassment.”
“With the squad they have and the players they have, the money they have spent, it’s not good enough.
“Mourinho has come up with plenty of excuses over the last few months, but there is no reason why United should shy away from dealing with these challenges.
“For a club like Man United to win the League Cup and the Europa League, with the teams that are in it, you would expect them to do that.”