The Red Devils secured their spot in the semi-finals of the UEFA Europa League on Thursday evening after recording a comprehensive 2-0 (4-0 aggregate) victory over LaLiga side, Granada, courtesy of goals from Edinson Cavani and a Jesus Vallejo own goal.
Pogba played a starring role in the encounter and registered the assist for Cavani's sixth-minute opening goal but, after picking up a booking for a strong challenge just minutes later, was brought off at half-time by his coach.
"Sometimes, Paul wants to win so much... he went into a couple of tackles after his yellow card but I thought I don't want to risk that [him being shown a red card] even though he played so well," Solskjaer explained, per BT Sport.
"We missed three [players through suspension] today and the season has been hard enough for us as it is."
Pogba, who captained United on the evening, acknowledged that he was at risk of being dismissed and revealed that he harboured no ill-feeling towards his boss hauling him off at the mid-way point of the match.
"Some tackles, a yellow card. I had to come off obviously." the French midfielder said. "The yellow card was unfortunate. It wasn't a yellow card for me but you have to accept it. We won the game, that's the most important thing.
"I know the foul just after it, I saw all the players trying to get me out. It's better that I came off before getting a red card."