Solskjaer was asked about comments made by Mourinho in September that United are worse this season than they were under his tenure.
“I’d rather not speak about other teams and other manager’s teams,” Solskjaer replied.
But he was happy to discuss the state of the club he inherited when he succeeded Mourinho in December 2018.
“I felt a lot needed to be changed,” Solskjaer said. “We’ve signed four players and lost quite a few and promoted from within, lots of youngsters.
“I don’t know how dramatic those changes have been. I don’t think it feels dramatic for the squad and the ones that were here. We needed certain pieces in the puzzle and they’ve worked.
“It’s not just about tactics, it’s about the players. I’ve got great staff. I’ve got a philosophy I think is worthy of this club. I’m a red and I think I know what this club needs.
He added that he was confident the club are now moving in the right direction.
“I believe we’re going places. I believe that we’re on the track that Man United need to be on. There are different cultures at different clubs and different ways of doing things, and I believe in the way we do things at Manchester United now.
“I don’t necessarily believe in everything we’ve done before, but at the moment I believe in what we’re doing. I think I’m the right man but I’m not going to sit here and talk about that. The proof is in the pudding at the end of the day.”
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