This match could've been seen as a last chance for Henrikh Mkhitaryan to fight for his place, playing in his favoured central position against lower league opposition, but once again he didn't have the best of halves. But Sam Winnall failed to profit as he dragged his shot wide.
Marcus Rashford found space around the box after combing well with Lingard in the 17th minute but his shot sailed over the bar.More news: Serena Williams withdraws from Australian Open
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Manchester United had the first attempt on goal through captain Pogba firing a straight shot at Carson in the second minute.
The barrage continued and Pogba wastefully side-footed wide with the goal gaping when following up Lingard's saved effort, before Derby finally yielded with six minutes to play.
Lukaku was next to head wide on 55 minutes, before Thomas Lawrence forced a diving save from Romero.
Not to be outdone, Lukaku then played a good give-and-go with Anthony Martial before tucking his shot under the advancing Carson to secure United's passage to the FA Cup fourth round.