The Three Lions secured qualification for the knockout stages of the World Cup after making it two wins out of two in Group G.
"He should take confidence by being backed by the England manager," Shearer said on Match of the Day.
"He played him in the first game, he's now backed him again and I'm pretty certain that if you see him get a goal then you'll see a different player. He has to because Rashford is now breathing down his neck.
"Two goals in 39 games is not good enough, he has to do better. So you'll see a different player [if he scores] but he needs a goal and he needs to start showing confidence and taking chances."
England will play Belgium in their last group game on Tuesday, with both sides on four points in the table.