Mourinho was sacked last month amid poor results and reports of dressing-room unrest, and his departure has seen United go on a run of seven successive wins ahead of Friday's FA Cup fourth-round clash against Arsenal.
Since being appointed caretaker manager until the end of the season, Solskjaer has inspired six consecutive Premier League victories and success in the previous round of the FA Cup.
United are now level on points with fifth-placed Arsenal in the Premier League and when asked about the decision to axe Mourinho, head coach Emery told reporters: "I was not surprised because I think they can win with normality.
"This team is with big players, who want to win the Premier League. This is normal. They can be in the position to win the league, but the reality is they have lost a lot of points this season.
"But now, they are very dangerous and in a good moment. Now, this team is different. I don't know why. But this team is different and they are playing with more confidence."
Training done— Arsenal FC (@Arsenal) January 25, 2019
How you all feeling ahead of Friday night's BIG game? pic.twitter.com/7tqMsf1YHI
Alexis Sanchez is set to make his first return to the Emirates Stadium since leaving Arsenal for United last January.
Sanchez has struggled to live up to the hype, however, with form and injuries seeing the Chile international score just four goals at United.
Former Paris Saint-Germain boss Emery, though, said: "He is a very good player and when I was at PSG, we thought he could help him.
"We did not because of the circumstances. We spoke about a lot of players, about a lot of important players, and one was the possibility of Alexis. But it was not possible."
"I don’t know why his performances or quality is better or worse in these circumstances," Emery continued. "Now, now, in the last matches, they are playing very, very well with very big performances.
"He's been starting on the bench after an injury but if he plays Friday, we need to work to stop him because he is a very good player."