The Norwegian was in charge of the Red Devils between December 2018 and November 2021, initially arriving as a caretaker manager before being handed the position on a full-time basis.
Solskjaer has detailed some of the issues that he faced at Old Trafford, claiming that some players turned down the opportunity to wear the captain's armband for certain matches.
"No one said 'No' to being the club captain, it was just for certain games. [On whether they said, 'I don't want to be captain for this match.'] Yes, but they didn't want to say it themselves, they had other people come up to me and say it," Solskjaer said on the Stick to Football podcast.
"It was disappointing. It's a different generation, its Gen Z. It's petty and shows a lack of ambition.
"Many players said no to doing the pre-match interviews, the three questions. You had the go-tos, Bruno [Fernandes] always did it, Harry [Maguire] always did it, Victor [Lindelof] did it.
"David [De Gea] did it, Luke Shaw did it. The others were worried about the questions, so preferred not to do it. You're scared of the whole reaction maybe, but you also understand some of the players' mental health.
"[On whether criticism from pundits and media affect players] Definitely, 100%. You criticise players or teams' tactics, but when it goes above that, because there are so many who watch and listen and go on social media [it does have an impact]. If they don't read it, friends, agents, managers will.
"When it gets personal, about character, they listen and think about it more than you think."
Solskjaer also revealed why he made Maguire the skipper during his time at the club rather than Fernandes, who is currently Man United's club captain under Erik ten Hag.
The Norwegian claimed that Fernandes can be "too passionate at times" and "loses a bit of control".
"I knew Bruno Fernandes had captain qualities when I was manager at Manchester United. He's got the personality and quality, but he knows and I've told him, that he's too passionate at times and he loses a bit of control," he added.
"I loved Harry Maguire as a captain, he was the leader in that group for me when I was at the club."
Solskjaer was sacked as head coach of the 20-time English champions in November 2021 off the back of Man United's 4-1 loss at Watford in the Premier League.