The QPR skipper saw red for a headbutt in the 36th minute.
Ref Neil Swarbrick did not see the clash but dismissed Barton on the advice of his assistant David Richardson.
Rangers were leading 1-0 at the time but their 10 men went down 2-1.Barton tweeted after the match: "Well feel for the officials, they've been conned. Linesman definitely never saw it, all he seen was Johnson's reaction.
"My head doesn't move forward at all. Ridiculous decision ? seen 25 replays."
QPR boss Neil Warnock blasted: "Who says cheats don't prosper? Bradley has conned him and we feel we have run over a few black cats.
"He has not been headbutted at all. Not in a million years.
"To go back like he did and then check his nose for blood was a disgrace.
"It's getting a fellow pro sent off. He should be done by the FA."
But Johnson had the last word at the world darts final at Alexandra Palace, with a sign saying 'Barton your breath stinks.'
NEIL WARNOCK says Bradley Johnson conned ref to get Barton sent off