The trio played no part in United's win at Old Trafford on Saturday evening, having all started in the EFL Cup semi-final defeat to Manchester City three days earlier.
Solskjaer made nine changes against Watford, naming Bruno Fernandes, Harry Maguire and Marcus Rashford on the substitutes bench among others, though Pogba, Lindelof and Shaw were not included in the matchday squad.
The United manager confirmed that all three were missing through injury in his post-match press conference, though was optimistic about Eric Bailly after the defender was forced off during the first half.
Bailly was substituted for Maguire after a collision with goalkeeper Dean Henderson left him dazed and requiring assistance to leave the pitch.
Solskjaer did not know the full extent of Bailly's problem but believed the issue to be with the 26-year-old's neck and did not suspect that Bailly suffered concussion.
"He got a good whack," he said. "I don't think it's concussion, hopefully a muscle injury and we'll have to check it tomorrow. Fingers crossed he won't be out for too long."
After the final whistle, Bailly confirmed his injury was only minor. "Good job by the team to advance in the FA Cup. I am OK, it was just a knock," he tweeted.
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