The Belgian striker had a frustrating performance in yesterday’s goalless draw at Liverpool and appeared to be slow in getting up the pitch after defending a set-piece, which played the Reds onside.
Jurgen Klopp’s team almost scored from the opportunity and it angered Allardyce, who pointed out how he dealt with a similar situation when he was Crystal Palace manager last year.
“If you see Lukaku, this is a typical centre-forward,” he said.
“He’s got his defensive responsibility in phase one. And then phase two ‘well I’ve got to get up the pitch now’.
“We had this a little bit with Christian Benteke last year and we’d say ‘no Christian, you’ve got to stay there’.
“If the ball drops to a Liverpool player, you must stay where you are and defend that second phase.
“So it certainly gave Liverpool a chance there.”
Liverpool would have taken the lead from the chance through Joel Matip had it not been for a world class save from David De Gea.
The Spanish keeper kept his eighth clean sheet of the season and Allardyce praised his technique in keeping the scores level.
He added: “You talk about technique and technique is about stopping the ball going in the net by whatever you’ve got in your locker.
“His speed of movement there to get that block was brilliant.”
The draw meant United lost ground on neighbours City at the top of the Premier League, but remain in second place.
Manchester United return to action on Wednesday with a trip to Benfica in the Champions League, before travelling to Huddersfield on Saturday.
