The England forward has struggled for form recently, firing a blank in the 2-0 loss to West Ham to extend his run without a goal in open play to six matches.
And Shearer believes the 21-year-old must sharpen up closer to goal to prove his worth in the absence of Romelu Lukaku, who joined Inter Milan this summer.
“United took a massive gamble when they sold striker Romelu Lukaku to Inter Milan and asked players who are either untried or unproven goalscorers to replace him,” Shearer said in his BBC column.
“Marcus Rashford has huge talent, but he still has a lot of improving to do. Mason Greenwood has huge potential, but it is a big ask for him to lead United’s attack at the age of 17.
“I have some sympathy for Rashford, who failed to score in open play for the sixth successive match this season, because it would not give me great hope of getting 25 or 30 goals if I was playing in that team – but he has got to help himself too.
“We still don’t know if the 21-year-old is going to end up as as a centre-forward, but if he is going to be a top-class striker with a killer instinct then his movement in the box needs to improve dramatically, and he needs to learn to score the ugly goals as well.”
Rashford will hope to return to the pitch soon after coming off at the London Stadium with a groin injury, but Ole Gunnar Solskjaer anticipates being without the forward for a “little while”.
“He felt his groin,” Solskjaer said. “We’ll do a scan tomorrow to see how badly he’s injured. I don’t know how long he’ll be out, I’m not a doctor. But he’ll probably be out for a little while.”