Uniteds top-four hopes suffered a major blow on Sunday as they were beaten 4-0 at Goodison Park.
Solskjaer apologised to Manchester United fans following a result which provoked brutal criticism from the likes of club legend Gary Neville.
And Pogba, who was widely criticised for his performance against the Toffees, has explained what Solskjaer said in the dressing room after the match.
[In the dressing room] we let the manager speak, the staff speak and they spoke the truth, Pogba said. They said what happened in the game and [said] it is not respectful for ourselves.
What we did on the pitch is not respectful for the team-mates, for the staff, for the people, for the kitman, for everyone. For their work, they put their life on us, the team and this club.
What we showed on the pitch, we did not give them the joy back and thats why we are angry with ourselves. We want to do better for sure and we have to. The reaction has to be there.
I want to say [to the fans], and I know it may not be enough, but the fans want a reaction from the players and the only way to apologise to them is to give everything on the pitch, do our best, create chances, score goals, defend, work for the team and we can even lose games, but with a good performance and pride on the pitch.
Thats how we should apologise, just to give everything for the club, for the shirt, for the team-mates and for ourselves as well because it is us on the pitch and we cannot perform like we did.
In an interview with Sky Sports, Pogba added: I wish I knew [what went wrong]. It was the details, the desire, we spoke about courage and everything we had when the manager came.
What we had there, it was just like another team and this is not good. It is not good for Man United, for the story of the club or for the fans.
It is not good at all what we did. Losing a game is something really bad that we dont want to when we are in the race for the top four and losing 4-0 as well.