The Bantams boss admitted that his side were lacking going forward, but insisted the linesman was at fault when they fell behind.
"We're a bit disappointed. I think we just lacked a little bit of extra quality in the final third but I have no complaints," he told BBC Sport.
"I was convinced the ball had gone out before they scored and I thought the linesman made a few mistakes."
However, Parkin went on to say that a draw was a good result in the end as the League Cup finalists appeared to be heading for a defeat.
"It could turn out to be a very good point because it was starting to look a bit desperate," he said.
"We had a big setback on Sunday because we felt we let ourselves down. It was important we followed it up with a performance today."