Bobby Grant gave referee James Adcock little alternative but to brandish the red card following a reckless challenge on former Dale defender Rory McArdle 35 minutes into the Spotland clash.
But City were unable to press home their numerical advantage against a stubborn home rearguard.
Parkin, a former Rochdale manager, admitted his side lacked sufficient quality in the final third to break down Dale.
"We are reasonably pleased with the performance and keeping a clean sheet is always important," he said. "Sometimes it can be difficult to play against 10 men, but we're not entirely happy with the quality in the final third.
"We had ample opportunities to score but we need to be more clinical in front of goal, so we're a little bit disappointed in that sense. If Rochdale had kept us to next to nothing then we'd have accepted a point, but we had ample chances to show a bit more quality in the final third to win the game.
"We started brightly and had a zip about us, moving the ball around with confidence. But we need that bit of luck at the moment, perhaps one to go in off someone's backside. Everything we strike at the minute seems to be getting blocked, so I'd like to see us bobble us one in."