Town hit the woodwork twice. David Ball's first-half effort rebounded off the crossbar before substitute Andy Mangan headed Dean Howell's cross against a post in the 69th minute.
Mellon said: "There wasn't much difference between the sides. We matched Bradford for long periods and we are disappointed with the result, but you have got to take your chances.
"We hit the woodwork, but there are hard luck stories all the time in football and you have got to make your own luck.
"You have got to take your chances at tough places like Bradford, but we will dust ourselves down and get on with the next game.
"There is a massive difference between the Conference and the Football League in the tempo of the game and how well organised teams are."