The Red Devils were thrashed 4-0 by the Toffees at Goodison Park.
And Solskjaer and his backroom staff were said to be infuriated by the performance, underlining a major overhaul is needed at Old Trafford this summer.
The Norwegian kept his players in the dressing room for more than half an hour after the abject display.
And the Daily Mail claim shouting could be heard in the corridors as United stars blamed one another for the defeat.
Players were said to be heated towards one another as United suffered a sixth defeat in eight games.
Yesterday, the Red Devils were subjected to video analysis of the diabolical display.
And the report claims that even the Manchester United chef gave the players a piece of his mind on the performance.
The Mail say insiders report the mood is as bad as when Jose Mourinho was in the latter stages of his reign at Old Trafford earlier this season.
And it has become evident that Solskjaer must be backed in the transfer market this summer if he is not to meet the same fate as the Special One.
United midfielder Paul Pogba branded the performance against Everton ‘disrespectful’ on Monday evening.
“We let the manager speak, the staff speak and they spoke the truth,” he told Sky Sports.
“We didn’t respect ourselves, the club or the fans.
“What we did on the pitch is not respectful for the team-mates, for the staff, for the people, for the kit man, for everyone. For their work, they put their life on us.
“What we showed on the pitch, we did not give them the joy back and that’s why we are angry with ourselves.
“We want to do better for sure and we have to. The reaction has to be there.”
United return to action tomorrow night in a crunch clash with arch-rivals Manchester City in the Premier League (8pm).