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Fernandes featured 58 times for the United as they finished second in the Premier League and reached the Europa League final.
He scored 28 goals and provided 18 assists in that time - but Solskjaer says he should've given the 26-year-old more chances to rest.
Solskjaer told ESPN: "Bruno last year... maybe I overplayed him but it was because he was so important for us."
United have bolstered their attacking ranks this summer with the signing of Jadon Sancho from Borussia Dortmund.
That alongside Jesse Lingard's return from a loan at West Ham United gives the Red Devils more options in attack.
He continued: "Adding these extra players - Jesse coming back, Jadon coming in, Anthony [Martial] being fit again - gives us a lot more to work with."
Fernandes returned to action with a wonderful free-kick in Saturday's 4-0 win over Everton.
Another player that supporters are keen to see more of this season is Donny van de Beek.
Arriving from Ajax last summer, many thought van de Beek would bring a new dimension to United's midfield.
The Netherlands international started just four games in the league last season and a summer transfer was even hinted.
But he's returned to pre-season training in phenomenal shape and United's coaching staff are said to be impressed.
Solskjaer added: "He's [van de Beek] put on a bit of muscle, yeah. He had last season to learn about English football, and he's used the summer well. You never know how players from abroad [are going to] come in -- some players need a year.
"You see Fred's development and evolution and there are other players that just come in and take to it straight away; it depends."
As well as Sancho, United have sealed the signing of Raphael Varane from Real Madrid.
When asked about the pressure big money signings bring on, Solskjaer replied: "You feel under pressure all the time. At this club, with this responsibility, it's not just clinging onto your job; it's about the responsibility that's in my hands.
"We've got millions of fans, the players, the club, the staff... and the responsibility is on getting results. As long as you get results and improve, that's what I felt that we've improved all the time. As long as you can see improvement."
Featured Image Credit: Man Utd & PA Images
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