The Red Devils signed the Belgium international in a £75m deal from Everton in the summer transfer window despite the lure of a potential return to Chelsea.
Lukaku has hit the ground running at Old Trafford following four goals in his opening four Premier League games to repay some of his transfer fee.
The 24-year-old scored 25 times in 36 games in the Premier League last season to finish behind Harry Kane in the goal-scoring charts.
However, Lukaku has limited experience in the Champions League to raise concerns about whether the Belgian forward will be a prolific goal-scorer in the Champions League.
Former Manchester United defender Parker warned the Red Devils that Lukaku will be the big weakness in Jose Mourinho’s team in Europe’s premier club competition.
“There’s a few players in that United squad who have very little experience at this kind of level, particularly in the attack: Lukaku, Marcus Rashford and Anthony Martial spring to mind,” Parker wrote in his column for Eurosport.
“Lukaku worries me a bit as the most important thing in Champions League football is ball retention and to kill the game, especially if you get a goal in front. Patience is vital. He doesn’t strike me as that kind of player – at least at the moment.
“It’s a very different task to playing in the Premier League where he is undoubtedly one of the best strikers of the past five years.”
Lukaku was one of three summer signings at Old Trafford in the summer transfer window after the Red Devils recruited Benfica defender Victor Lindelof and Chelsea midfielder Nemanja Matic.
Manchester United finished in sixth place in the Premier League table last season but still qualified for the Champions League thanks to their Europa League success.
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