James Hanson put the Bantams ahead after five minutes, nodding in Raffaele De Vita's cross, but Tom Clarke headed the hosts level shortly after the half-hour mark.
Bailey Wright sent Preston in front after 68 minutes but the lead was short-lived as Rory McArdle netted the game's fourth headed goal, before Hanson had another headed effort disallowed late on.
Parkinson, whose side looked the more likely to snatch a late winner, also reserved special praise for former West Ham winger Kyel Reid, who enjoyed a productive night.
"I can't be unhappy with a point at all," he said. "We've bounced back after two difficult results and we've responded. I'm happy with what the team and the club have done.
"I felt we should've got something out of both of our last two games but we didn't and we got beat but I was delighted with our response. Even when we went 2-1 down we kept playing and we were top class.
"It represented what we are all about as a group of people. The task now is for us to keep on doing that in each game and if we do then we'll do well this season.
"Kyel Reid gives us that outlet with his pace and I thought he was brilliant.
"It was a great occasion, we've got thousands of fans behind that goal and it was a brilliant surface to play on and two good sides playing good football."