Both sides were controversially reduced to 10 men early on when Virgil van Dijk and Paul Paton were dismissed by referee Craig Thomson, while Scott Brown and Nadir Ciftci were lucky to avoid further sanctions.
Van Dijk was sent off for a stamp on Calum Butcher, which Butcher reacted too but it was a case of mistaken identity as the official flashed the red card at Paton instead.
United boss McNamara told Sky Sports: “I was disappointed with the initial challenge that sparked the whole thing off. I thought it was reckless from Scott Brown. Nadir’s reacted and a few things happened after that.
“Paton will feel very hard done too, especially with the incident with Aberdeen earlier in the season. He’s a bit unfortunate with decisions.”
The drama continued to play out as both sides hit the post – first Ryan Dow then Anthony Stokes – before United were awarded a spot kick after Stokes was adjudged to have fouled Aiden Connolly in the box.
Ciftci, who was lucky to still be on the park after aiming a kick out at Brown which sparked the earlier dismissals, dispatched the spot kick past Craig Gordon.
Celtic were then awarded a penalty of their own as Dundee United were reduced to nine men after Paul Dixon handled Griffiths’ shot, but the former Hibernian striker was thwarted by Rado Cierzniak from 12 yards.
However, Griffiths atoned for his earlier miss, with an excellent guided header beyond the Dundee United goalkeeper to bring the Hoops back on level terms and set up a fourth encounter in a fortnight against Jackie McNamara’s side.
Ronny Deila said after the game: “It was a tough game but we created four or five big chances and should have won it. We’re still in it and at home so that’s a positive thing.”
The Norwegian said he hadn’t seen the incident which saw the two players dismissed but on the United spot kick, he said: “We didn’t have pictures of the fighting but saw the penalty. You see what you see it is a dive of course.
“I think we are the only team in Scotland who has had a suspension for diving. Derk Boerrigter got two or three games but I haven’t seen it happen thereafter.”
