Tranmere boss Ronnie Moore accused Bradford manager Phil Parkinson of getting "carried away by Wembley" following Rovers' 1-0 win.
The duo had been involved in a war of words in the first half of Sunday's encounter when Parkinson thought Rovers skipper Ian Goodison should have been sent off for elbowing winger Kyel Reid.
Victory over last season's League Cup finalists, only their second of the campaign, moved Rovers off the bottom of League One.
But when Moore applauded the Bradford section of the Valley Parade crowd at the end, he claimed Parkinson told him 'enjoy your win, but don't take the Mickey out of the crowd'.
Moore said: "I was upset by that - him telling me what to do. It looks as if he is getting carried away by Wembley and winning promotion."
Moore also accused Bradford of trying to get Goodison sent off.
He added: "Ian Goodison's booking had nothing to do with Reid going down. Their manager got involved when he shouldn't have done.
"Phil Parkinson shoved Ian Goodison and Goodison has got booked for shoving their manager. The referee has seen one shove, but not the other."
Parkinson was convinced Goodison should have seen red and said: "As soon as it happened I was certain it was going to be red, but the fourth official said it was a forearm rather than an elbow - that is why it was a yellow rather than a red.
"My feeling was that it was a straight red."
The winning goal from Ryan Lowe in the 67th minute brought fourth-placed Bradford's eight match unbeaten league run to an end.
In a game of few clear-cut chances, Lowe broke the deadlock by beating keeper Jon McLaughlin with a low, angled shot into the far corner after Jake Kirby had flicked the ball into his path.
"It was a great finish," said Moore. "That is what he is about. He is a top-class finisher - he comes alive in the box.
"We got tired towards the end when Bradford threw everyone forward, but our keeper made two great saves.
"We defended well when we had to and the players have done everything we asked of them."