The 24-year old, who moved from Everton for £75m last week, scored 25 Premier League goals for the Toffees last season.
But Sheringham says that the Belgian will have to get better in some areas in his game, namely holding the ball up and eluding deep-lying teams.
"It's a funny one playing for top teams," he told talkSPORT. "I'm not saying Everton aren't a top team but when they played, other teams came onto them and left a lot of space in behind and left Lukaku [able to play] at his best, exploiting a lot of space.
"When you play for the big teams, the top six teams, other teams come and camp in their own half and there isn't any space in behind for you to come in and run into, using those big strong legs and body. It's all a little bit more intricate.
"It will be very interesting to see how Lukaku gets on there. He will have to change his game a little bit. He's not the best at holding the ball up, but he's still a young man and he'll have to learn to change his game and play for top club."