The second-placed Gills pulled off a classic smash and grab raid, with in-form Cody McDonald grabbing his third goal in four league games since re-joining the club on loan from Coventry.
But Bradford dominated the first half and Parkinson felt they should have taken something from the game.
He said: "James had two heading chances - one in the first half and one in the second. You have to hit the target with those and he knows it.
"He has shown in the past that he is capable of doing that. They were defining moments in a game where there was a very thin dividing line between winning and losing.
"We dominated the first half and it lifted the opposition that we were not ahead at half-time. We gave away a very cheap goal, which is frustrating because I felt they were there for the taking. You would have to be honest and say promotion is slipping away.
"It was a big game but we have two 'cup-finals' before Wembley - at Wycome and Wimbledon - and we have to make sure we scrap for every ball in those."