Ole Gunnar Solskjaer is short of striking options as Marcus Rashford has been ruled out for several weeks through injury.
And the Norwegian sensation marked his debut for the German giants with a stunning hat-trick off the bench.
His impact there is considered by Ince to be another example of the failings that are costing United.
He told Paddy Power: “A new signing in January has become a must. It’s not that they need to – they absolutely have to.
“It kind of makes Erling Braut Haaland even more embarrassing and a pain in the arse than it already was, especially after we saw his debut hat-trick.
“Because if they don’t sign someone, who’s going to get you goals?
“We saw the sitter that Anthony Martial missed against Liverpool. It’s simply not good enough. He should be burying that, if that had fallen to Rashford I’m confident that would’ve been a goal.
“With Rashford out, you can’t trust Martial will make up those goals. Mason Greenwood is great, but he’s young, untried and untested. You can’t put that level of pressure on such a great player.”
Solskjaer remains in the market for attacking additions during the January window, but finds his ranks depleted at present, after letting Alexis Sanchez and Romelu Lukaku leave for Inter in the summer.
Ince added: “If Ole wasn’t already regretting letting Romelu Lukaku go, he seriously will be now.
“I’ll be the first to admit that I had a go at him at times, and he can’t retain the ball, but you do get 20-25 goals a season from him.
“United let him go without replacing him and now they’re paying the price. Hindsight is a wonderful thing but, really, Ole should never have let him go.”
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