The England striker went down very easily when he attempted to go around Latics goalkeeper Ali Al Habsi in just the fourth minute of the match that ended 4-0 to United.
Referee Michael Oliver awarded a penalty to the home side which Al Habsi managed to save from Javier Hernandez which was a decision which infuriated Martinez who feels Welbeck should have been sent off for a challenge on Franco Di Santo later in the game.
"I have come to United three times before today and for whatever reason we don't seem to be measured in the same manner as the team at home," said Martinez.
"Today the penalty is as bad a decision as you are going to see in the Premier League. In many ways, you feel as though you are fighting against a mountain.
"There were tackles flying around that if they had been the other way round there would have been a couple of red cards.
"For Danny Welbeck's last challenge, his foot was over the ball on Franco. It is completely reckless. Under the new regulations you cannot do that. It is a red card, for a Wigan player, Manchester United, everyone."