The Millers were leading 2-1 when referee Darren England indicated there were eight minutes of stoppage time to play at the AESSEAL New York Stadium after goals from Jon Taylor and Richie Towell overturned Fernando Forestieri's opener.
England allowed play to continue well beyond that period and Dominic Iorfa struck a last-gasp equaliser that stretches Wednesday's unbeaten run at the home of their South Yorkshire neighbours to 43 years.
Warne, whose side deserved to win, is at a loss to explain where the official got the extra time from.
Asked whether he would try to seek answers with England, the Millers boss said: "It makes no difference, it's a waste of breath. He'll apologise or something and I'll just say 'OK' politely.
"I just don't get it. I had a digital watch on, I asked him how long, he said eight minutes. I respectfully accepted it so it is tough to take.
"In fairness we should still see the game out. I could go and speak to the referee now but I don't know if I have the gumption to do it.
"I don't know where the extra time has come from. If there is extra time on the eight then I don't know where from. There was no injury, no goal, no substitution. I was going to make a substitution because I thought he would just add another 30 seconds on."
The Millers would have climbed out of the bottom three with a win, which would have been their first in the Championship since New Year's Day.
"I'm disappointed with the way it ended but it doesn't detract how proud I am of the performance," Warne added.
"I thought we were excellent. The only criticism I have got is that we didn't take the chances we had."
Steve Bruce, unsurprisingly, took an opposite view, believing the referee was entitled to add extra time on following the lengthy injury to Jordan Thorniley.
The Owls boss did, however, question Forestieri's red card that came when he picked up two bookings in the aftermath to his side's leveller.
"There was a legitimate reason we were playing 10 minutes. Jordan (Thorniley) was down and when there are head injuries like that, the referee is entitled to add time on," Bruce said.
"There is nothing quite like scoring late on. It was one of those strange ones: he went down in the 87th minute, there was still three minutes to play and then he added on the eight minutes. He was quite legit in what he's done.
"I'm not too sure what he's done afterwards with Forestieri. To pick on Forestieri because he is alone with the supporters, he could have sent off my whole team. The 17 of them were in the away end.
"That's what football fans want to see, that it means something to the players.
"Now we are faced with not having him next week, for what? Totally ridiculous.
"All of a sudden we won't be able to have him next week, for celebrating with supporters. What is all that about? When someone (Michael Ihiekwe) has tried to break him in half on the halfway line. It didn't make sense to me."