May picked the same team that drew at Celtic Park the previous weekend but they were sluggish from the start and Jon Daly added a hat-trick to David Goodwillie's opener to earn United a convincing fourth consecutive victory.
Falkirk substitute Pedro Moutinho headed home in injury time but there were few Falkirk fans left inside the stadium to see it and most of them booed their team off the park.
And a forthright May was in no mood to shield his players from public criticism.
"I think it was the players' responsibility," he said. "Did I do anything different from last week? No. I'm not going to protect them, they were absolutely murder.
"Can I go and motivate them? They motivate themselves like I motivate myself every single morning.
"When I was a football player, I did the same myself. On the odd occasion, I played like that. They have to take responsibility.
"The application was not good enough, the quality was not good enough. There are no hiding places."
May revealed he had just asked the players some simple questions rather than castigating them in the dressing room, but his anger was apparent."
He added: "I have seen it in football for years, managers protecting players.
"They have to take responsibility and they never did that. I'll take the boos from the fans, no problem at all, but they have to stand up and be counted as well.
"If they want to play here as long as I'm here, that's what they will have to do.
"People say 'you might lose the dressing room'. Well, if I've got the dressing room like that, I would rather lose the dressing room.
"Everybody knows me in there, I treat them with respect and I treat them right. All I ask for is effort and application, and I certainly never got that today."
United caretaker manager Peter Houston refused to make any definitive statements on his future after leading the team to a fourth successive win.
Houston ruled himself out of the running to replace Craig Levein after United lost 7-1 at Rangers in the week leading up to Christmas, but they have now won four consecutive matches.
Houston said: "I'm certainly thinking that, long term for the football club, it might be better to bring someone else in.
"I like my coaching and training. When I worked with Craig, I knew what my job was.
"I'm not going to say I will take it to the end of the season. I'll take it game by game and see what they say upstairs."
Source: Team Talk