A minute from the interval, with the game goalless, Reid suddenly unleashed a tremendous left-footed shot from 30 yards which screamed past home goalkeeper Richard O'Donnell.
And before Smith's half-time instructions could turn things around, James Hanson beat the offside trap to collect a long ball from Rory McArdle and hammer home a low shot to give the Bantams a two-goal cushion which proved enough.
Smith said: "You can't do anything about a strike like that. It was a wonder strike into the top corner, but we should have done better with their second goal.
"Goals always change games. It's disappointing because we felt we could get something out of the game and some of our play in the second half was outstanding.
"I'm not going to be disheartened losing to Bradford. We all saw what they did last season. If we keep performing like that we shall win more games than we lose.
"In the last half-hour I thought it was as good as we have played all season and if we had scored then we should have got another."