Solskjaer was put in charge until the end of the season after Mourinho was dismissed on Tuesday with United 19 points off the top of the table.
That change paid instant dividends as United scored five goals in a Premier League match for the first time since Alex Ferguson's last game in charge back in May 2013, thrashing Cardiff 5-1 on Saturday.
"I don't think he (Solskjaer) has stopped smiling," Young said after victory in the Welsh capital.
"He was like that as a player. He always has a smile on his face and I think that can reflect down on to the team, which is a good thing.
"Ole has come in and we were preparing in the right way for a game, even though it's been a crazy week."
Mourinho clashed with a number of senior figures in the United dressing room over his two-and-a-half seasons in charge.
Paul Pogba quickly deleted a controversial social media post of him smiling with the message "caption this" in the hours after Mourinho's departure.
Restored to the starting line-up for the first time in four league games, Pogba was instrumental in setting up four of United's five goals on Saturday.
"No celebration at all. Absolute lies," Young said at the suggestion players were delighted to see the back of Mourinho.
"Obviously it was disappointing for the manager to get sacked.
"In his two-and-a-half years he won trophies. We have to take some responsibility for that as we are on the pitch.
"But we have to move on from that. As professional players we have to get on with the job in hand, and that is what we did here."