The Red Devils hope that none of the ailments will prove to be too serious.
They are about to hit a two-week break with no domestic action to take in, but a number of their star turns are due to head off with their respective countries.
The 23-year-old played the full 90 minutes at Goodison Park, as did Lindelof, but Shaw was replaced by Axel Tuanzebe with 23 minutes to go.
Solskjaer is now waiting on fitness updates for all of his walking wounded, with the Norwegian less than impressed at having to take in a lunchtime kick-off on Saturday after making a midweek Champions League trip to Istanbul.
The United boss told MUTV when asked if any problems had been picked up in a welcome win over the Toffees: “Yes. Victor's back, Marcus's shoulder, Luke Shaw's hamstring. That's three I can remember from the top of my head.
“I hope everyone else is okay. David didn't play [in midweek] but he had a groin problem before the game.”
He added on the scheduling of a visit to Merseyside: “Give us another 24 hours or 26, 28 hours to recover and you'll get a better game from us.
“The first half was top. Get on the ball, play and the goals we scored were fantastic.
“In the second half they went into survival mode because they're tired, they're on their knees but fair play to them.
“You could see, of course, Scott [McTominay], Fred, Victor didn't play [on Wednesday], Juan [Mata] didn't play the full game in Turkey. You could see they've got legs but the others were down on their knees.”
While fatigue proved to be an issue for United, Solskjaer was delighted with the application from his team – with three points helping to ease some of the pressure that had been building on his shoulders.
The Norwegian said: “If we can get this determination, mindset, approach every single game, we'll be hard to play against.
“You see all the tackles that Scott and Fred were winning in the middle there, we're tight, we're compact, we win the ball, we play, we've got spaces, that's how we want to see these boys. So we're very pleased with that. I can’t praise the boys enough for the character that they’ve shown.”