In the scathing assessment of the 5-0 drubbing at Old Trafford, O'Hara suggested Harry Maguire 'looks like he is towing a caravan' and that his teammates do not work hard enough for one another.
Solskjaer's position has come under increased scrutiny after a 5-0 defeat against their biggest rivals at Old Trafford.
United were poor throughout as Mohamed Salah hit a hat-trick, with goals from Naby Keita and Diogo Jota adding to the embarrassment for Solskjaer and his players.
The Norwegian boss said the defeat saw United hit 'rock bottom' but believes he is the right man to continue at the helm.
However, former Spurs midfielder O'Hara insists the players deserve their fair share of scrutiny for failing to deliver against one of United's biggest rivals.
"Manchester United were an absolute disgrace yesterday," O'Hara said. "Oh my God, defensively, they were a disgrace.
"I'm actually going to take back my statement saying that Harry Maguire is world class. From this season, he is not world class.
"He is miles off it, he looks like he is towing a caravan! So it was a really poor performance from them yesterday, but before the Ole Gunnar Solskjaer pile-in - because I know everyone is going to do that today - you have to address the players.
"The players are nowhere good enough to be playing for Manchester United right now. Their lack of intensity as a team is embarrassing, they don't run.
"They are good enough, talent-wise, but in terms of running and desire and determination to run around for a Manchester United team, they are not good enough.
"None of them work hard enough out of possession, their set up as a team out of possession is a disgrace.
"I look at that Manchester United team and I think probably only Luke Shaw, maybe [Marcus] Rashford are doing that. None of them sprint, in and out of possession, none of them do that."
The 'Baby-Faced Assassin' was appointed on a full-time basis in March 2019 after initially coming in as interim boss in the wake of Jose Mourinho's dismissal.
Things turned sour under the Portuguese at Old Trafford, with squad harmony seemingly hitting rock bottom as his man-management skills came under scrutiny.
Solskjaer certainly restored the feel-good factor to the Red Devils initially, but is yet to enjoy serious success at the club where he achieved legendary status for winning the 'Treble' in 1999.
Given how rivals Jurgen Klopp, Thomas Tuchel and Pep Guardiola have discernibly advanced the tactics of their respective sides during Solskjaer's reign, O'Hara questioned just how much the Norwegian can take this faltering side.
He added: "I think everyone knows that tactically, he is not there as a manager when you look at Guardiola, Tuchel and Klopp.
"Ole Gunnar Solskjaer is not at that level. I think the players do want to play for him; we saw that against Atalanta, they could have downed tools on him in that game and put more pressure on him.
"But they came out in the second half and they got him a result. They're not good enough tactically and I don't know what philosophy they are trying to play, they style of football, the identity of Manchester United, I don't think as a team they know.
"They want to press, but they're not good enough to press, so they don't really know what they are doing.
"As a manager, we all know it, Ole Gunnar Solskjaer is out of his depth. I look at the team and I question what he wants out of the side.
"Mourinho got slaughtered for killing Luke Shaw's career and they said he wasn't a good man manager, but Solskjaer is doing the same thing to Donny van de Beek, he's doing it to Jadon Sancho.
"But because he is a club legend, he doesn't get any stick for it."