In front of estimated 2,000+ away supporters, second half goals from former Rochdale midfielder Jason Kennedy and City top scorer James Hanson were enough to pick up the Bantams' second away win of the season.
Parkin said: "We are delighted with the lads in every aspect really.
"This game (vs Rochdale) probably wasn't one we wanted after Wednesday night and Leeds because we know that Rochdale are an energetic side that do test you physically.
"Rochdale have the ability to move the ball quickly and really make you work but the lads were magnificent today (Saturday).
"We fully expected the boys to be able to handle playing Wednesday and then Saturday but you never quite know until you get out there and play the game.
"The lads seemed to get stronger as the game went on, which is testament to their fitness.
"They showed real tenacity to stay in the game in the first period and then real quality in the second half to keep the ball well and score a couple of good goals.
"This is a very good win for us. Rochdale have had a couple of good results recently so we delighted to come here and get the win.
"We are delighted for the fans as well. They have dipped their hands in their pockets again today after the Leeds game and come here to support us in numbers.
"We know it can be expensive following a football team so we really appreciate them turning up in their thousands once more - we are so pleased we can send them home happy with three points."