Adebayo Akinfenwa and Curtis Weston struck either side of half-time to extend the Gills' unbeaten run to nine games and give Hessenthaler's men a desperately-needed three points in their promotion push.
Although Jackson, who took charge of his first game after Peter Taylor stepped down as Bantams boss last week, was disappointed with the timings of the goals, he was buoyed by some of their play.
He said: "I'm really disappointed with the result. Sadly, we've come away from home and not got what we deserved.
"We didn't deserve that at all, but we gave away goals on 43 and 46 minutes. Anyone knows if you're conceding on the stroke of half-time and then right after it, you're asking for trouble.
"But I'm pleased that the boys really dug in, they passed the ball well and they gave it a good go. I'm trying to get the team to express themselves more than they have been doing so far this season."
Source: PA
Source: PA