Wan-Bissaka received a straight red card in the latter stages of the first period when he caught Christopher Martins after losing control of the ball.
Solskjaer has admitted that it is "hard to argue against the referee", but the Norwegian believes that the nature of the defender's follow-through could have made it a booking rather than a red.
"That's a little bit the astroturf, Aaron gets a touch that's too far and he gets the ball but he follows through. It's hard to argue against the referee but then he didn't go through his ankle, he hit him on the top of his foot," Solskjaer told MUTV.
Cristiano Ronaldo scored his third goal since returning to the club in the 13th minute of the contest to make it the perfect start for the 20-time English champions.
However, Moumi Ngamaleu levelled the scores for Young Boys in the 66th minute before Theoson-Jordan Siebatcheu scored the winner for the home side in second-half stoppage time after a loose pass from Jesse Lingard.
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