The 22-year-old was brought on in the 64th minute with the scores level in United's 1-0 FA Cup third-round replay win over Wolves.
Within three minutes, the hosts were in front thanks to a clever through ball from Anthony Martial and a mini-chip from Juan Mata.
Yet it came at a heavy cost as the England international lasted just 16 minutes before being replaced by Jesse Lingard due to a back injury.
Inexplicably, that substitution came several minutes after Rashford initially pulled up.
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United could have played briefly with 10 men, but instead left Rashford on the pitch while Lingard warmed up near the Stretford End.
"That [delay] was because Jesse was down in the corner flag," Solskjaer told a press conference after the game.
"So any moment, a tie like this can go into extra time and that would have been even worse. So he had to stay on just for two minutes to get the ball out and there was no chance he was going to be able to run.
"He's a quick healer and he'll play through some pain, definitely, if he's capable and it's not a bad, bad injury, but we've seen that he's struggled lately."
When asked if he was worried about Rashford, the Norwegian added:
"Yeah of course. I didn't want to play him.
"I think he got a knock to his knee in his back, but he's been struggling for a little while, that's why we've kept him away today.
"But we needed the win, he was involved in the goal - so that was a positive - but it backfired. We will do everything we can to get him fit for Sunday."
Technically speaking, he didn't actually touch the ball in the build-up to the goal though he did leave it for Martial, but that's an argument for another day.
To give Rashford credit, he didn't complain about being kept on and played through the pain for several minutes, tweeting after full-time:
"Never want to feel like I’ve let my teammates, the club and most importantly the fans down so did my very best to carry on tonight and was gutted to come off. Top work from the lads to get into the next round."
With 22 goals for United and England already this season, he'll be a huge loss if he doesn't make it to Anfield. It's a daunting enough trip for Solskjaer's men as it is.
It makes the manager's decision not to haul him off immediately even more bizarre, but maybe that's just indicative of Solskjaer's desperation to win silverware this season. United played a strong team for the replay against Wolves, only making three changes from the side that beat Norwich 4-0 in the Premier League.
The FA Cup is, after all, probably their best chance with their Carabao Cup hopes hanging in the balance after a first-leg thrashing by Manchester City.
They could be in for another if they head to Merseyside without a man who has been head and shoulders above the rest this season.News Now - Sport News