The Belgian striker was at fault for Manchester City’s second goal at Old Trafford after he failed to clear his lines and Nicolas Otamendi capitalised to net the winner.
Lukaku, who signed for Manchester United from Everton in the summer transfer window, also missed a clear-cut chance to net an equaliser for Jose Mourinho’s men late on.
The 24-year-old forward has only scored twice in his last 10 games for Manchester United this season.
And Neville felt that it was an afternoon to forget for the striker in the Manchester derby.
Speaking to Sky Sports after the game, Neville said of Lukaku’s defending for City’s second goal: “He just makes a mess of it, Lukaku.
“It just sums up his day – the way it went for him all the way through. He was rash.
“He’s just got to compose himself. It’s a bad time to make a mistake in a game like this.”
He continued: “You look at Lukaku today, and he struggled. He struggled out there. I’m not just talking about missing a chance. He struggled to actually be in the game, his confidence.
“He’s got to get over that quickly because he’s a Manchester United centre-forward.
“He’s a young lad and he’s got to get to a stage where he believes he should be out there. It’s as if he doesn’t believe he should be out there at this point in the season.”
Manchester United had equalised on the stroke of half-time thanks to Marcus Rashford’s goal after David Silva had put the visitors in front.
The Red Devils are now 11 points behind Manchester City in the race for the title as they bid to try and get themselves back into the title race in the coming weeks.
Mourinho’s men return to Premier League action on Wednesday night with a home clash against Bournemouth at Old Trafford.
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