The initial incident that rankled with Martinez happened in the first couple of minutes during United's 4-0 win, when Welbeck went down under Ali Al Habsi's challenge.
It seemed innocuous at the time, and TV replays showed there had been no contact as Welbeck went to ground.
Javier Hernandez missed the penalty but later in a feisty contest, Welbeck lunged in on Franco di Santo, which Martinez felt warranted a red card.
"For Danny Welbeck's last challenge, his foot was over the ball on Franco," said Martinez.
"It is completely reckless.
"Under the new regulations you cannot do that.
"I am not arguing whether they should be in the game or not. That is for others.
"But with the laws as they are, you cannot tackle people like that.
"The foot is over the ball. It is reckless and dangerous.
"It is a red card, for a Wigan player, Manchester United, everyone."
Despite that, Martinez did not blame referee Michael Oliver for his side's defeat.
But the Latics chief admitted he was irritated at that first spot-kick call, which he felt set the tone for the entire afternoon.
"I was (irritated)," he said.
"You could see it. You know what he is trying to do.
"I have come to United three times before today [Saturday] and for whatever reason we don't seem to be measured in the same manner as the team at home.
"Today [Saturday] 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."
United's biggest win of the season was scarred by a short burst of anti-Liverpool chanting from a small minority of home fans.
Sir Alex Ferguson had expressed the hope that a line could be drawn in the sand on the sour relations between the two sets of supporters following this week's damning report on the handling of the Hillsborough tragedy in 1989, in which 96 people died.
It is a feeling shared by all senior figures at Old Trafford, who can only hope Saturday's songs are not repeated when United head to Anfield on Sunday.
"The manager has made the club's position very clear on this matter," said United.
"It is now up to the fans to respect that."
United said they "deplore" such songs.
For all the furore, United eventually claimed their biggest win of the season, which allowed them to capitalise on the failure of Chelsea and Manchester City to collect three points.