Dundee United manager Peter Houston will complain to head of referees John Fleming after a yellow card shown to Jon Daly by Iain Brines.
Houston believes the United striker was booked for a similar foul to one which Beram Kayal earlier escaped punishment for during Celtic's 4-1 win.
"When I asked him about it after the game, the referee said, on another day, it would be a yellow," said Houston.
"I will be on the phone to John Fleming tonight asking, what's that about?"
Kayal's foul came shortly before half time, with United already trailing to a 23rd-minute strike by Gary Hooper.
And Houston had an angry exchange with Brines at the final whistle following Daly's yellow card for a foul on Charlie Mulgrew, the manager revealing that the referee gave him an explanation for the decisions when they had words in the tunnel.
"What confuses me is the fact that, in the first half, Conway nicks a ball past Kayal and Kayal takes him down," said Houston.
"To me, that is a booking. Jon Daly does the same thing in the second half and I don't uunderstand it.
"'On another day, that would be a yellow card' - what does that mean?
"I don't know what it means, but I think it is two exact same fouls. But he didn't see it that way."
Houston nevertheless conceded that title-chasing Celtic were the better side and that his own players had contributed to their own downfall.
The United manager could not understand why midfielder Morgaro Gomis, instead of advancing, had sent the ball back into his own half to Garry Kenneth, who subsequently set up the opener with a poor pass.
"I have no complaints about the result," said Houston. "I think Celtic were the better team.
"In the first half, we didn't keep the ball. We didn't pass the ball well at all, which we came here trying to do and we have players who can do it.
"But we rushed passes and gave the ball away cheaply.
"And, without Celtic being brilliant, they've got a goal gifted to them.
"Garry has owned up for the mistake at the first one."
Second-half strikes from Kayal and Kris Commons set Celtic on the road to victory before substitute Johnny Russell pulled one back in stoppage time.
However, there was still time for Celtic replacement Daryl Murphy to expose United's defence once more in a defeat that all but ends the visitors' hopes of catching third-placed Hearts in the Scottish Premier League.
"So the defensive performance has got to be looked at and I need to look at that again," added Houston.
"I know it is late in the season, but Daryl Murphy picks the ball up for the fourth goal, for instance, on the halfway line and there are four orange jerseys around him and he runs the distance and scores.
"Now, Darryl Murphy is not blessed with the greatest amount of pace, but we stood off him and allowed him to dictate to us.
"They were poor goals we lost, so I am gutted with that.
"We came here with no pressure on us, wanting to go and play and pass the ball and get the crowd silent.
"But we never did it. We actually created more in the second half after we went 2-0 down - the belief started to come into the team."