United go into Sunday’s match with Tottenham, 19 points off the top of the Premier League.
Jose Mourinho led the team to League Cup success in January and their Champions League qualification hopes are now hanging by a thread.
Keano was used to challenging for top honours.
The Irish hardman won 17 major trophies with the Red Devils under Sir Alex Ferguson – he lifted the Premier League trophy seven times, the FA Cup four times and the Champions League once.
Keane says: “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.
“He [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.
“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.”
Keane also questioned the role of United skipper Wayne Rooney, who has struggled for playing time this season.
He says: “Wayne needs to be playing regularly, to keep in shape and stay on top of his game.
“If he is going to be a bit-part player at United then forget about it. He has got to move on.”