Warnock branded Johnson "disgraceful" after taking offence to comments the Robins boss made in the local press before the game.
Johnson said: "We have to make sure we win it, whether we do it through aggression, good football or intimidation, we have to make sure we do it. I make no apologies for that."
The Millers boss was incensed by those comments, which he read out from a cut-out of the article in his post-match press conference, and labelled Johnson a disgrace while also referencing a previous spat with Johnson's father Gary.
Neil Warnock addresses the media after the 1-1 draw at Ashton Gate earlier this evening. #rufc pic.twitter.com/JgZzXxpXAg— Rotherham United (@OfficialRUFC) April 5, 2016