Parkinson got a standing ovation from City fans on only his second game back at the club since his exit in 2016.
The history-making former Bantams boss was chuffed with the reaction from a whopping 21,552 home crowd.
But he was less impressed with referee Ross Joyce for turning down a “stonewall” spot-kick after Paul Mullin appeared to be caught by Sam Stubbs.
“How the ref hasn’t given that is incredible,” said Parkinson. “We could all see that the lad’s slid in, caught him and pulled him down.
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“It’s an absolute stonewall penalty. It’s 100 per cent a penalty but you’re also crying out for better protection in open play for Mulls.
“I thought he got pushed into the hoardings in the second half but it is a physical game.
“That’s how we like it but I think when the ref looks back at it, he’ll see that it was a clear pen.”
Mullin headed Wrexham in front before Adam Wilson grabbed a well-deserved point for City with a late equaliser.
Parkinson added: “It was a hard-earned point. We knew it was going to be a feisty encounter coming here with a full house.
“It was fast and furious at times and, of course, when you go a goal ahead you want to take the three points.
“But we had to withstand pressure second half and the way we defended our box was outstanding.
“Did we get hold of the ball as much as I would have liked in the second half? Probably not but when you don’t do that you’ve got to be physical in and around your box.
“Away from home against anybody, you know there are going to be periods when you’ve got to defend and particularly here.
“I’ve managed here a lot and kicking to that Kop, when it’s full like that, it almost sucks the ball into that end.
“We had to withstand crosses coming into the box and in the main I thought the lads defended them incredibly well.
“There was just one little moment which has proved costly but I’m pleased with the point.”
I had five great years and loved every minute
Parkinson was clearly moved by the warmth shown by the City fans as he walked along the touchline before the game.
“Steve (Parkin) and I had five great years here and loved every minute of it. That meant a lot.
“It was a great occasion coming out with the ground packed and it was two good sides out there.
“To be fair to Bradford, they were in the play-offs last year and have probably underachieved and started a little bit slow.
“But we know they’ve got good players. (Andy) Cook at the top of the pitch got 30 goals last year and he’s a real threat.
“We knew they’d look to press us and play with energy like they had done at home against Swindon. We knew it would be difficult.”
