They struggled with their delivery from wide areas, and Daley Blind was a particular culprit.
Leicester City, meanwhile, had a disappointing start to the season, after losing to Arsenal at Emirates 4-3 despite a good fight back.
Rashford replaced Juan Mata and made an impact within three minutes. Just 10 minutes later Marouane Fellaini, another one of Mourinho's substitutes, doubled their lead. Zlatan also believes he can play well with Lukaku.
England global Jamie Vardy has scored two goals in the opening two fixtures and he will be Foxes' biggest threat against United.
The recently retired Jamaican sprint king, a three-time Olympic champion across both 100 and 200 metres, might have reached the Riyad Mahrez long free-kick that Jamie Vardy almost collected between Phil Jones and David De Gea in the 12th minute.
"We scored from a corner that I didn't even see because I was speaking with Lingard", the United boss said.
United want to make the Theatre of Dreams a fortress once more after dropping points at home on a more frequent basis since Sir Alex Ferguson's retirement in 2013. Though he moved well into space for his teammates, his final ball (particularly his crossing) was too often inaccurate.
Wes Morgan and Jamie Vardy start for Leicester after recovering from knocks that they suffered against Brighton & Hove Albion.
Paul Pogba and Nemanja Matic will operate in the middle.
"They have not played the minutes they would have liked so far but they are all being very patient and waiting for their opportunity to become important for the team". He appears truly liberated in his play so far this season.
Lukaku's shot was parried by Schmeichel and converted by Mata on the rebound, only for the assistant to disallow the strike in a marginal call, much to the frustration of the Spain worldwide. His clever movement was crucial to wearing Leicester down.
The remainder of the third round ties will be played over the week commencing September 18.
Martial performed well and caused a number of problems driving forward. Cut inside often looking for the final ball, and though he did not score, his dribbling and movement were key in breaking down Leicester's resistance.
He said: "I think he understands me and to be honest I understand him because in the beginning of last season, if he understands me better, he would have started better, but if I understand him better, probably I would help him in a faster way than I did".
Huddersfield remain unbeaten and second in the table after dominating their game against Southampton and David Wagner's side are yet to concede a league goal this season.
Who will come out on top in the battle of the managers José Mourinho or Craig Shakespeare?
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