The Belgium international was initially linked with a move back to Chelsea in the summer transfer window as a replacement for Diego Costa.
However, Manchester United managed to hijack Chelsea’s proposed deal to sign the 24-year-old striker to bolster their attacking ranks.
Lukaku completed a £75m move to Old Trafford to become Manchester United’s second most-expensive player of all-time.
The Belgian forward has already opened his Manchester United account with a close-range finish in a 2-1 loss to La Liga giants Real Madrid in the Uefa Super Cup.
Lukaku scored 25 times in 36 games in the Premier League last season – only Tottenham Hotspur striker Harry Kane scored more times in the top flight than the Manchester United signing.
The Red Devils drew 10 of their 19 games at Old Trafford in the Premier League last season in what a dismal home record in their first campaign under Jose Mourinho.
Former Liverpool defender Carragher is confident that Lukaku can help Manchester United to improve their home form this season.
“The big problem last season was scoring goals at home against the lesser teams,” Carragher told The Debate on Sky Sports.
“Lukaku is superb at that. He will score plenty of goals at Old Trafford. He gets questioned in big games.”
Manchester United start with the 2017-18 campaign with a home clash against West Ham United on Sunday afternoon.
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