Martial was given the chance to lead the line against the Hammers, with Cristiano Ronaldo left out of the squad, having been heavily involved since his return to the club.
The France international played the full 90 minutes against David Moyes's side but struggled to make his mark, as the Red Devils exited the competition in the third round.
Dublin, who played for Man United between 1992 and 1994, said that Martial's body language "is horrible to watch", and the 52-year-old also criticised the forward's work-rate.
"We need to see more from Anthony Martial, we have said it many times before but he is not helping his cause. I want to see him sweating and putting the ball in the back of the net," Dublin told BBC Sport.
"He has not done enough since being at United, you see flashes and think it is the start then he doesn't do anything. His body language is horrible to watch, he doesn't want to run around and work hard to be Manchester United's number nine."
Martial, who was linked with a move away from Old Trafford over the summer, still has three years left to run on his contract with the 20-time English champions. body check tags ::