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."
Gills manager Martin Allen, who saw his side record their 10th away win of the season, said: "It was another fantastic away performance. There were some outstanding individual displays but they were also tremendous as a unit. It was a great end to a week that has not been so great.
"Monday's home defeat against Wycombe hit us hard. Bradford are in a cup final, having beaten Premier League sides Wigan, Arsenal and Aston Villa, so for us to come here and win was pretty good going. Yesterday we had to train in the dark at Leeds' training ground because there was a crash on the motorway, so our preparations could have been better."
Hanson headed inches over the bar from Kyel Reid's cross in the 26th minute and it needed a superb double save from Stuart Nelson to foil Bradford captain Gary Jones and top scorer Nahki Wells.
Bradford keeper Matt Duke didn't have a shot to save until Chris Whelpdale tested him with a low drive after 52 minutes but the Bantams were caught out 12 minutes later. Vastly experienced Deon Burton lobbed the ball over the defence and McDonald fired past the stranded Duke.
Hanson wasted his second chance on 78 minutes from another Reid cross and, although Bradford applied considerable pressure during four minutes added time, they couldn't conjure up an equaliser.