Manchester United sacked Mourinho in December with the Red Devils stuck in a rut at the time, sitting 11 points adrift of the Premier League top four.
Initially, Solskjaer hit the ground running as interim boss, winning 14 of his first 17 games.
Manchester United’s form nosedived towards the end of the campaign, though, with the Red Devils ending the season on a run of two wins from 12.
And, speaking on the club’s pre-season tour of Australia, Solskjaer has admitted he inherited a squad low on confidence.
“I saw many things that we tried to improve on. The players had the quality, but I felt the confidence wasn’t the highest,” he said.
“They’d just lost to Liverpool with a bad performance.
“We just tried to tell them how good they are, how important a position they have in the club’s history and that they were signed because they’re all quality players.
“No-one signs for Manchester United without having quality.”
Solskjaer also admitted he feels honoured to be United manager and is trying to emulate Sir Alex Ferguson in the Old Trafford dugout.
“It is at times,” said Solskjaer when asked if it felt surreal.
“It’s such an honour but it’s also a great responsibility. I’m following some great managers.
“Sir Alex was the best and I’m trying to take the best from him and put my own personality on the job.
“We’ve got such a big fanbase and such a history, that I feel it’s a fantastic opportunity for me.
“I come in at 7am, thinking I’m the first one in and Michael Carrick and Kieran McKenna are already there, planning the sessions.
“I know this club is going places because of the people we have here.”
United are next in action against Leeds on Wednesday, where they will be hoping for a second win of the tour.
The Red Devils breezed past Perth Glory on Saturday courtesy of goals from Marcus Rashford and Jimmy Garner.
After Leeds, then they travel to Singapore to face Inter Milan.
And, after that game, they face Tottenham in Shanghai before returning home.