United were outclassed by the Ligue 1 leaders in a 2-0 Champions League loss at Old Trafford on Tuesday, recording a single shot on target and conceding to second-half Presnel Kimpembe and Kylian Mbappe goals.
PSG were missing strikers Neymar and Edinson Cavani, but the French champions had the squad depth to still find a way through and give United their first defeat in a European tie on home turf by a two-goal margin.
"I can't do anything about Alexis Sanchez", said Solskjaer after the match.
Sanchez was preparing to come on for Lingard, who had strained his left hamstring towards the end of the first half in the 2-0 Champions League defeat.
"Mourinho wanted discipline from everyone and that is defendable as well and so that's maybe (why) Pogba, as we have seen in recent games, has performed well".
"It's a hard mountain to climb but it's not impossible", said Solskjaer.
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"I think there has to be some realism in terms of where this group of players are at". United need a coach to make a difference at this level, in the way that Tuchel did by overcoming injury and tactical headaches to secure victory.
Prior to the goals, Di Maria was waiting to take a corner in the first half and several bottles were thrown in his direction - the Argentine reacting by picking one up and pretending to drink from it. "He plays and that's competition and that's fair competition in my opinion".
The injuries come at a bad time for United, who have a number of important games in the coming weeks including the FA Cup fifth round clash with Chelsea this Monday (February 18) and the return leg with PSG on March 6. "It was a nice comeback for him, I'm very happy for him and of course he helped us a lot".
"It was a new system and we weren't really used to it", Mbappe said.
"You can see that we've not played games at this level for a while and we'll have to learn from this experience", said Solskjaer.