A humiliating 4-0 loss to Everton left the new Manchester United boss fuming and questioning whether some of his squad care enough.
And he promised that they will not win a power struggle with him like they did with former boss Jose Mourinho.
Two days after admitting that some players needed a reality check, Solskjaer was asked whether those players care enough.
After pausing for six seconds, he said: “I don’t know. You have got to ask them. I have asked them. Of course if you want to play at this club, it has to be more.
“I want my team to be the hardest working team in the league, that is what we were under Sir Alex [Ferguson].
“You can’t change your whole squad. One step at a time. I am going to be successful here and there are players who won’t be part of that.”
United have now conceded 48 Premier League goals, comfortable their highest ever tally in a single season and their most in a top flight campaign since 1978-79 when they leaked 63.
But Solskjaer was fuming after a performance in which they were outrun by Everton and offered nothing going forward until a solitary shot on target five minutes from time.
“We have got to apologise to the fans because they were absolutely fantastic but that performance is not good enough for a Manchester United team
“We let the fans down, we let the club down. That performance is difficult to describe because it is so bad. They beat us on all the basics, long throw in, our corner, they counter attack.
“We were beaten on all the ingredients you need, added to the talent. There is no place you can hide on the pitch. That is just 85 minutes before we got a strike on target which is not good enough.”
Not for the first time Solskjaer criticised his players fitness admitting their efforts to drag themselves back into contention in the race for a Champions League spot may have taken their toll.
But he called for a reaction in their remaining four games starting with Manchester City at Old Trafford on Wednesday.
He added: “We need 75, 76 points to get top four and we are on 64, 12 points to be won. It sounds too easy to say we have to look forward but we cannot dwell too much on this.
“In the long term we have to look at this but in the short term we have to look at City.”
Everton boss Marco Silva insisted his side were the “best team on the pitch” from the first minute to the last.
“We never give them the chance to feel comfortable. We give a quiet afternoon for our goalkeeper. We work as a team since the first minute and score nice goals also,” he said.
“Even if you expect a reaction from them, we keep doing the same ad fully deserved the three points.”