The Premier League side were beaten 2-0 by their League One opponents, courtesy of an own goal from John O'Shea and a second-half strike from former Sunderland man Jon Stead.
Without the rested Jermain Defoe, Sunderland struggled to provide a goalscoring threat and were comfortably beaten in the end, as Bradford continued their remarkable FA Cup adventure that saw them dump out Chelsea in round four.
In his post-match press conference, Poyet accused the media of failing to accurately report his remarks, which he feels has turned supporters against him.
"If we close Sunderland - if we put a China wall around the city - it would be fantastic," he said. "When we let you [the press] in and you get [back] out and say what you want, then we've got a problem.
"The problem is you [the media] not me. If you write what I say the fans would be on my side."
