All six goals came in the first half but it was the visitors who always looked in the ascendancy.
Terry Gornell put Dale ahead before Alan Connell scored the first of two penalties. Andrew Tutte and Ashley Grimes both struck before Connell netted again from the spot, with Gornell doubling his tally before the break.
"We were second best today," Parkinson said. "I have got to hold my hand up as well - the balance of the team wasn't right.
"Rochdale played very well, but the disappointing thing was that we didn't pass the ball at all in the first half. So the ball came back all the time and you are back under pressure.
"We can pass it well, but we didn't do that and found ourselves 4-2 down. We didn't get the ball down and play and therefore we were not going to create chances.
"Teams come to Bradford, they know we have beaten Arsenal in the League Cup and it is a big game for them. Rochdale played with an edge to their game and whether their early goal gave them that belief I don't know, but we lacked intensity in all departments."
Bradford visit Morecambe on New Year's Day and Parkinson said: "We will respond to this. We have got to make it one-off."