The Terrors boss was handed an immediate three-match suspension for a touchline clash with St Johnstone counterpart Tommy Wright during a Scottish Premiership fixture.
United intended to contest the ruling until they learned that doing so could delay the ban and prevent McNamara from taking his place in the dugout for the Scottish Cup final.
"We firmly believe that there are solid grounds to appeal the sentence imposed. However having given the matter further thought and as no hearing date has yet been fixed, we now believe it is in the best interests of all concerned to accept the sentence imposed and withdraw the appeal," said the club in a statement.
United will take on St Johnstone in the cup final on May 17.