A late Jodie Broughton try salvaged a 20-20 draw for Salford after five league defeats in a row - but boss Phil Veivers felt a controversial decision by referee Richard Silverwood cost the Reds victory.
Shaun Ainscough looked offside when he collected Ben Jeffries' kick in the 73rd minute and sent Tom Burgess over to make it 20-16.
Veivers said: "To say it was offside is the biggest understatement of the year.
"The players say the touch judge called offside and the ref didn't give it, which makes one wonder.
"I thought we were playing Aussie rules at one spell."
Salford snatched a draw when Bradford had Olivier Elima sin-binned three minutes from time and Broughton went over in the corner from a pass by Luke Patten.
Daniel Holdsworth missed the conversion and Veivers added: "If he'd popped the kick over we'd have won but it wasn't the missed kick which cost us the game.
"Conditions didn't help either side with persistent rain and a gale-force wind.
"Our completion rate was 82% in the first half but then we made two errors which led to tries.
"We got in an arm wrestle in the second half but Luke Patten did well after taking a knock on the ankle early on.
"He carried the ball strongly from the back and Danny Williams took his tries well."
Karl Pryce scored a hat-trick of tries for Bradford, whose coach Mick Potter said: "We came up with some pretty poor decisions in defence but Salford are probably saying the same.
"I'm not satisfied with our performance and we weren't smart enough at the right time.
"Oliver Elima's sin-binning was a pretty tough call but I didn't think Tom Burgess' try was offside.
"The ball was in the air three or four seconds and Shaun got there quickly."