Mark McGhee believes Dundee had a case for a penalty in the dying moments of the game, with the ball appearing to hit the arm of Celtic ace Jota.
The Dark Blues fell behind to a late Giorgos Giakoumakis goal and that looked to be the end of the action until the visitors had a final surge forward.
Cammy Kerr played the ball in to a packed Celtic box with Jordan McGhee and Jota jumping for the header. But the ball seemingly hit the on-loan Benfica forward’s arm as he attempted to head clear.
Despite protests from Dundee players, referee Gavin Duncan waved play on.
‘It hit a hand’
Mark McGhee, who watched his first game as Dee boss from the stands, felt a spot kick could have been given, but he had no complaints about the overall result.
“I don’t know what the technicalities of it are,” he said. “But it hit a hand and I’ve seen it on the video lots of times.
“But I think the referee said the boy who headed it, head it on to his own hand.
“I mean, don’t ask me, in my day if it hit the hand it was a penalty.
“But I’ve got no excuse with that.
“We didn’t lose really because of that.
“Celtic are a terrific team at the moment and they are likely to beat you.
“We’re more interested in our own performances than anybody else’s.”
Dundee opened the scoring through Danny Mullen on 26 minutes.
But they found themselves behind in the space of minutes with Giakoumakis bagging a quick-fire double to put the hosts 2-1 at half-time.
The visitors stunned the Parkhead side for a second time with Ryan Sweeney heading in to make it 2-2.
It looked like Dundee were going to hang on for a point but up popped the Greek forward on the 86th minute to complete his hat-trick and send the Dark Blues home empty-handed.