The Belgian striker has made an impressive start to his Old Trafford career in the Premier League after a return of four goals in four games in the Premier League.
Lukaku scored Manchester United’s second goal in a 2-2 draw with Stoke City at the bet365 Stadium on Saturday evening ahead of the visit of the Swiss champions.
The 24-year-old doubled Manchester United’s lead with a close-range header following Marouane Fellaini’s opener to secure three points from their opening Champions League game.
Substitute Marcus Rashford sealed three points with a late goal to help the hosts make a perfect start to their European campaign.
Former Manchester United midfielder Hargreaves, who was part of Sir Alex Ferguson’s side that won the Champions League in 2008, was impressed with Lukaku’s goal.
“Just what he needed,” Hargreaves told BT Sport.
“Two great crosses, Two great headers. Lukaku just wanted it more. He is that big physical presence. It was a terrific header.”
Lukaku moved to Manchester United in a £75m deal from Everton in the 2017 summer transfer window after the Red Devils managed to hijack a deal to sign the striker ahead of Chelsea.
The Red Devils have already beaten Swansea City, West Ham United and Leicester in the Premier League so far this season.
Manchester United haven’t won the Premier League title since 2013, while the Red Devils last got their hands on the Champions League crown in 2008.
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