Wilkie, who lost three years from his career with knee problems, stayed down after a tackle by Hoops' striker Scott McDonald but when the ball went out for a goal kick, Dougal waved play on.
After United keeper Lukasz Zaluska then kicked the ball out, Wilkie was allowed treatment as Dougal and Levein had a pitchside confrontation.
Celtic returned to the top of the SPL after goals from Glenn Loovens and Georgios Samaras were enough to hold off a spirited United comeback who reduced the deficit through David Robertson.
But the game was almost incidental as Levein left Dougal in no doubt what he thought of him.
"He lost his composure, stuck his finger in my face and told me to shut up," the United boss said. "It wasn't acceptable.
"In all my time in football, no other referee has ever done that.
"I have lost all respect for him after the way he spoke to me.
"If it happened in the pub on a Saturday night to any of you guys, the guy would have got a punch in the face."
Levein continued: "I asked him why he didn't stop the play for Lee Wilkie to get treatment and I don't think that is unreasonable.
"If you were Lee Wilkie and you had been out of the game for three years, you would be upset.
"It is compounded by the fact that he wouldn't let anyone come on, he didn't believe him.
"If he wants to look at the stud mark above Lee's shin he can do that."
Wilkie claimed Dougal made a "silly" retort when he asked the referee why he had failed to allow him immediate treatment.
The United skipper said: "McDonald caught me just below the knee, I don't think it was intentional but I still got caught.
"I was waiting for him to stop the game but he waved play on.
"He thought nothing had happened and it looked like he wasn't going to let the physio on.
"I said to the referee at half time, 'what were you playing at?' and he said, quite arrogantly, that his kids had had bigger knocks than that, which was a stupid comment to make - his kids must be some size.
"All he needed to say was that he thought I never got touched but he had to make a silly comment.
"I told him that my knees were bad enough without getting any treatment but he didn't seem bothered.
"It was my good knee, not my left knee, but I got a fright and he should have been aware of the problems with my knees.
"Referees want respect from players and they treat them in that way and that's what annoys us."
Levein, who was delighted with his side's performance, was also aggrieved at Loovens' goal which came from a Shunsuke Nakamura corner.
He said: "McDonald held and blocked the keeper. He does it every week and he is good at it.
"But that is part of the game, I just hopes that it would get spotted but it didn't and they scored."
Celtic manager Gordon Strachan was wary of commenting on the Levein/Dougal spat, just saying: "I seen what happened."
However, the former Coventry and Southampton boss claimed his side were "spooked" after United threatened to come back from a two-goal deficit in the same way they had in January.
The champions held on for the victory which takes them one point ahead of Rangers who play Hibernian at Easter Road tomorrow night. But Strachan believes he was almost alone in thinking his side would not capitulate to the Taysiders again.
"I liked what I seen for the first hour but it was a long 25 minutes at the end," he said.
"They took their goal brilliantly but defensively we were very annoyed.
"We were 2-0 up against United before and they got it back to 2-2.
"Our guys and our fans realised it could be the same thing happening again so we all got a bit spooked by it.
"They were all thinking, 'it's going to happen again,' although I didn't think it would.
"Dundee United felt better because they had been in that position before and felt that they could do it again.
"So they took heart from that and became the more dominant force in the game."