Stuart McCall has warned his unbeaten Bradford City side they face tougher challenges ahead in League One.
A 19th-minute goal from former Leeds United striker Dominic Poleon was enough to earn the Bantams all three points against 10-man Gillingham.
Alex Jones saw his cut-back guided into the net by Poleon, who whould have netted a second but fired wide after rounding Tomas Holy.
The hosts finished with 10 men after Conor Wilkinson was red carded with 15 minutes remaining, for a foul on Timothee Dieng.
McCall said: “Getting six points from six is obviously great but we know we can do better.
“We did enough to win the game but we set standards and we look for more.
“We are still gelling as a side and still looking for our ideal shape but, having said that, the scoreline could have looked more comfortable if we’d taken a couple more of our chances.
“Better game-management from us once they went down to ten men could have seen us wrap up the game earlier. We were a bit sloppy on the ball at times and we gave away a few too many free-kicks, especially because that was a good chance for them to score.
“We’d have been kicking ourselves if their late goal for offside had denied us two points.
“We have picked up the win and the clean sheet, which is great, but we know there are tougher challenges ahead and we must improve. We will have a good week on the training pitch this week, so we can work on a number of things.”
Gillingham: Holy, Ehmer, Zakuani, Lacey (Eaves 63), O’Neill, Byrne (Nash 89), Martin, Wright, Ogilvie, Parker (Wagstaff 89), Wilkinson. Unused substitutes: Hessenthaler, Oldaker, Cundle, Hadler.
Bradford: Doyle, McMahon, Kilgallon, Knight-Percival, Field, Law, Dieng, Reeves, Jones (Gilliead 58), Patrick (Taylor 67), Poleon. Unused substitutes: Sattelmaier, McCartan, Pybus, Devine, Robinson.
Referee: J Busby (Oxfordshire).