Manager Sir Alex Ferguson has warned improvement must be swift if the Red Devils are to avoid a derby-day humiliation at Manchester City on Sunday .
A veteran of 271 games for United and 18 England appearances during a 14-year career that also encompassed three seasons at Leeds, Greenhoff was a rock-solid defender widely regarded as one of the best of his generation.
And what he watched from his former employers in last Saturday's 4-3 win at Reading was enough to make him scream at the television.
"There was an issue about the Reading players attacking the ball, which the United players didn't seem to do," he said.
"But the thing that baffled me was why Patrice Evra was defending a corner by standing in front of the keeper but behind a 6ft 2in centre-forward.
"Why would a goalkeeper accept someone being in there?
"Alex Stepney would have just shoved me out of the way if I had done that. It didn't offer the goalkeeper any room."
Yet Greenhoff can do nothing constructive these days, having called time on his career in 1984 after an ill-fated spell playing for his brother Jimmy at Rochdale which created such bad blood between the pair that - apart from one brief interlude - they have not spoken since.
The origins of the row are chronicled in his autobiography 'Greenhoff', which offers absolutely no prospect of a reconciliation.
It seems a shame, since the pair were - until Gary and Phil Neville came along - the most famous brothers to don a United shirt.
Not that it will spoil Greenhoff's enjoyment of Sunday's showdown at the Etihad Stadium, the type of game in which he would love to have been involved.
"If you can't look forward to these sorts of matches, you shouldn't be playing the game," he said.
"I looked forward to every match. There was nothing better than running out at Old Trafford.
"In fact, I don't like this business of walking out together. I would want to walk out to boos at the Etihad. It would make me feel welcome."
Indeed, one of Greenhoff's chief moans about the present era is the sanitised nature of the grounds, in which away followings have been slashed and the atmospheres usually suffer as a result.
"The grounds weren't as good, neither were the pitches, the balls or the boots," he said. "But the atmospheres were better.
"Sometimes you go to Old Trafford and it's quiet.
"How many United fans will be at the Etihad? Two thousand? It is pathetic.
"City used to get the entire Scoreboard End at Old Trafford. It was great."
Nevertheless, Greenhoff will still follow his normal routine on Sunday; same seat on the sofa, same pose, same slippers probably, hoping United can break the cycle of City success in the fixture.
"I used to love derbies. Now I hate them," he said. "I can't do anything about them. That is what bugs me. I can't kick anybody. It never leaves me. I don't suppose it ever will.
"I am sure there will be fans making sure they put the right socks on, or are wearing the right shirt. Some of the players will be like that and I am just the same."
However, after recent defensive frailties, Greenhoff's expectations are not high.
"I would take 0-0 now," he said.
"It would be a point better than last season at least. That first 6-1 game was a farce because of the sending-off (of Jonny Evans). The second (1-0 City win) was one of the worst derbies I have ever seen.
"This match will be a good one if United score first. But if City do they will just sit back and try to hit them on the break."