Scholes questioned why Carrick and other members of Solskjaer's staff were still in place after the manager's sacking on Sunday.
After victory at Champions League opponents Villarreal last night, Carrick said: " It has been a few emotional days. And the first one I talked to was Ole to see what he thought of it, because I thought it was the right thing to do. I am proud of the responsibility to take the team."
Scholes said yesterday: "I would almost be ashamed to be a part of the coaching staff now, after what happened to Ole. I think everyone should have left.
"They were part of Ole's staff, Ole trusted them every week by letting them prepare the team, and they have let the club and the players down as much as Ole has."
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