The Rhinos were clinging to an 18-12 lead when the 35-year-old former Bulls captain was shown a yellow card by referee Phil Bentham three minutes from the end and Bradford immediately took advantage of the extra man to score the equalising try through substitute Adam Sidlow. Peacock had to be consoled by McDermott after the final whistle.
"I won't be having any words with JP telling him to wind his neck in," McDermott said.
"He cares immensely. I don't know what he said to the referee but, in a game as heated as that, I would hope the referee hasn't been precious. If you can't cop a verbal from a 35-year-old bloke who's been playing for 15 or 16 years in the heat of the moment there, it would be a shame.
"If he's been out of order and very offensive, then it's probably the right decision but, knowing JP, I don't think he would have been overly offensive."
Leeds had made the best possible start, full-back Kallum Watkins scoring the opening try after just 24 seconds, but the Bulls stormed into a 12-6 lead thanks to tries from centre Adrian Purtell and second-rower Tom Olbison. When Peacock charged over on 52 minutes, the game looked to be heading the Rhinos' way but Bradford rallied superbly.
"We lost too much possession," McDermott added. "There's not much whingeing to be done when you lose so much unforced ball. Credit to Bradford, they fought and didn't allow us to get to get two scores in front. If we had been, it would have been less attainable for them."
Leeds skipper Kevin Sinfield had what would have been a match-winning drop goal ruled out because of a push by Peacock and he was wide with another attempt. The draw was just reward for Purtell, who scored his first try since suffering a heart attack in the aftermath of his last meeting with Leeds 10 months ago.
"It's been great to get him back playing the game he loves but there are special times to get a try in a big derby," said Bradford coach Francis Cummins. "I'm pleased with the way the game went. The lads earned the right to play. We didn't have enough quality at times, which was a bit frustrating, but boy have they got character.
"When you think about how we started the game, it was like we had half a dozen of our players left on the bus and we could have been blown away. At times it was ugly for us but we found a way, which was really pleasing. We lacked a bit direction but there was no lack of effort."