Solskjaer switched to a five-man defence in the second half after Aaron Wan-Bissaka's red card, but the Swiss champions were still able to fight-back from a goal down to hand United a defeat on the opening night of the Champions League campaign.
Despite the result, Solskjaer insisted it had been the right decision, a view backed up by his captain Harry Maguire.
"The signs were there last in five minutes of the first half that they were going to get get crosses in the box," said Solskjaer.
"Raphael [Varane], Victor [Lindelof] and Harry coped with it well. It was the best way of controlling them, but we should have done more with the ball."
Maguire and Lindelof started the game at centre-half, but when Wan-Bissaka was sent off after 35 minutes for a reckless challenge, Diogo Dalot was brought on for Jadon Sancho immediately before Solskjaer brought on a third centre-back, Varane, at half-time.
United were ahead at the break thanks to Cristiano Ronaldo's goal before Moumi Ngamaleu's equaliser and United States national team player Jordan Pefok's last minute winner following a lack back pass from Jesse Lingard won the game for Young Boys.
"I think the majority of their chances came late in the first half when we were playing a back four and we couldn't really get out to stop the crosses, we couldn't defend the box well enough with the number of bodies they were throwing forward into the box," said Maguire.
"And then we've come out in the second half and we looked controlled without the ball, without being a huge threat on the counter-attack. We could have done more on the ball but without the ball, they didn't really create big opportunities. The first goal is unfortunate, the deflection, I don't know who it ends up going in off.
"The last goal is a mistake, it happens in football, but it's unfortunate again. In terms of the shape without the ball, I felt it was a lot better when we went to a back three or back five. With the counter-attacks, we could have done a little bit more."