The former Accrington Stanley boss, who has never lost a match as a manager at Valley Parade, said: "We showed a lot of quality.
"The first half was a great advert for League Two football, the quality of play and the quality of goals. I don't think people give credit to the football played in League Two and League One.
"If that had been Barcelona playing football like we did in the first half people would have been raving about it. Obviously, we are not going to play to the same level as Barcelona, but you can still have the same desire and the same mentality.
"When we pass the ball like we did here we are up there with the best sides in the league. We are one of the best sides in the league going forward and this match showed that. Everyone knows about our defensive frailties, but when we play like that going forward we can beat anybody."
Coleman singled out striker Terry Gornell, scorer of two of Rochdale's goals, for special praise.
He added: "Terry was absolutely fantastic. It isn't just the goals he gives you, he runs himself into the ground."
This defeat ended promotion-chasing Bradford's run of five unbeaten league matches, but it was only Rochdale's second win in seven, both victories coming in their last three matches at Cheltenham and Bradford.
Now Coleman, whose side were relegated from League One last season, is looking for more consistency.
"We have turned in some really poor performances this season and it frustrates the life out of you," he said.
"But we have 17 new players in the team this season and it is always going to take time."
- Sports & Recreation