On his debut for the club after signing only on Friday, Cole latched onto Rory McArdle's ball into the box in the final minute of injury time to steer home from close range and send the home fans into raptures.
The goal secured City their first league win of the new season.
Parkinson said: "It was a fantastic moment for us.
"Devante hasn't even trained with us yet but the timing was right to get him out there this afternoon.
"He got himself in the danger area at the right time and got the ball in the back of the net for us - it was an important goal."
City supporters can watch Phil Parkinson's FULL post-match interviews this season on Bantams Player HD.