Lacey was shown a second yellow card for dissent as United were chasing a late equaliser.
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After the 2-1 loss, the youngster posted to social media: "I want to apologise to all of my teammates staff and the fans.
"I let everybody down tonight I shouldn't let my emotions get the better of me I will do everything I can to make this right (praying emoji)."
The result means United have only the Premier League left to compete in just halfway into the season.