The World Cup victor was far from his best in the defeat against Brighton, something which drew criticism from Paul Scholes.
Allardyce believes Martial was not good enough for Jose Mourinho's side and the France worldwide has not improved in his style of play since joining the Old Trafford club in 2015.
Meanwhile, NAIJ.com had earlier reported that English Premier League giants, Manchester United, suffered a shock 3-2 defeat to lowly-ranked Brighton in a tough Premier League tie played at the Amex Stadium. We thought Paul Pogba might be the ideal candidate to be that leader but he wasn't there today.
Scholes, who represented United for nearly 20 years, was critical of United's display on the south coast, but reserved much of the blame for Pogba.
Pogba, 25, has been rewarded the captain's armband in the absence of Antonio Valencia for the start of the new Premier League season by manager Jose Mourinho.
"I hope that is lost in translation", he said during his punditry role on Match of The Day.
"Some people need to talk for fear of being forgotten".
'Paul Scholes should become sports director and advise Woodward to sell Pogba.
"He had another really poor game".
But with Pogba's comments after their 3-2 loss to Brighton detailing his "attitude was not right during the game", Mills believes Sir Alex, who left Old Trafford in 2013, would have been less tolerant.
"Pogba's playing the ball out of play, he's overhitting passes, he's hitting passes short, he's getting caught in possession".
However, there was little sign of Pogba leading United out of the mire as he and summer signing Fred, who cost a reported £52.5 million (RM275.9 million) struggled to control the game in midfield.