The Belgian forward has been getting used to life at Old Trafford since signing for the Red Devils from Everton in the summer transfer window.
Lukaku, however, once again drew a blank in a big game when Manchester United crashed to a disappointing 2-1 defeat by Manchester City at Old Trafford last weekend.
The 24-year-old got back on the score-sheet on Wednesday night when he fired the Red Devils to a 1-0 victory over Bournemouth at Old Trafford in the Premier League.
Lukaku has been in decent goal-scoring form for the Red Devils so far this season but he has been criticised for failing to deliver in the big games for the Red Devils.
And former Liverpool FC midfielder Redknapp believes that Lukaku still has plenty of work to do to prove himself as a key player for the Red Devils.
Redknapp told Sky Sports: “Romelu Lukaku was back on the scoresheet in midweek, scoring the winner against Bournemouth, but disappointingly he was once again unable to affect the big game last weekend, in the defeat to Manchester City.
“Eric Cantona, Wayne Rooney, Cristiano Ronaldo, Dwight Yorke, Teddy Sheringham, Robin van Persie, Ruud van Nistelrooy… the big strikers at Old Trafford affected the big games. That’s what gets you the statue outside the stadium.
“Lukaku will score against West Brom this weekend, I’m sure, because he’s a flat track bully. But he’s got to change that perception of him. When you cost a club £80m you need to put in big performances in the big games.
“If he wants to get to the next level, that’s what he needs to do. It’s not about being overly critical of him. It’s just fact.
“He could score a hat-trick against West Brom and we wouldn’t learn anything about him.
“He has to start affecting these big games and showing us what he can do on the big stage.”
Manchester United are currently preparing for their Premier League clash against West Bromwich Albion at The Hawthorns on Sunday afternoon.
The Red Devils are aiming to get themselves back into the title race after falling way behind Manchester City.
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