United will be without the midfielder for the clashes with Hull, Sunderland and Stoke.
Nicholls was playing in his first match back following two months out with a knee injury and a second operation since his summer arrival from Luton.
Dennis Wise had argued the offence should have warranted a second yellow for Nicholls, who had been booked for a foul two minutes earlier, but after further consultation club officials have decided against lodging an appeal with the Football Association.