Arsenal lost 2-0 at Stamford Bridge but it was Costa’s tangling with their defence that most offended the manager.
Television replays showed the intimidating Brazil-born Spaniard pushing Laurent Koscielny in the face during tussles in the Arsenal penalty area in the first half.
“I think it’s unacceptable what he does to Koscielny. He pushes him down, he hits him in the face. I do not understand Mike Dean’s decision at all. Why does Diego Costa stay on the pitch and Gabriel is sent off? ” Wenger said at his post match briefing.
He added he felt Costa always acted belligerently and often got away with it.
“He will do the same next week and it’s always the same, he is always provoking.”
Wenger conceded that Gabriel deserved his red card for kicking Costa in a melee of protesting players at the end of the first half.
“Gabriel is guilty for getting involved of course he should not have reacted at all,” he said.
“ We expected that kind of game. We were not surprised but I expect the referee to make the right decision.”
Wenger also suggested the foul that led to Chelsea’s first goal, headed home from a free kick by centre back Kurt Zouma in the 53rd minute should not have been given. “It was hardly a touch,” he said.
Arsenal’s woes were compounded when Santi Cazorla was sent off after a second yellow card in the 79th minute leaving Arsenal vulnerable to Eden Hazard’s stoppage time strike that took a deflection off Arsenal substitute Calum Chambers wrong-footing former Chelsea keeper Petr Cech, playing for the opposition for the first time after his 11-year career at Chelsea.
There is no love lost between Wenger and his Chelsea counterpart Jose Mourinho, who, as if in retaliation said he felt Costa was man of the match.
The managers set the tone of the encounter by shaking hands while barely looking at each other at the start and Wenger disappeared quickly down the tunnel at the whistle without acknowledging the Portuguese.
Wenger’s Arsenal have failed to beat a Chelsea team managed by Mourinho in the Premier League in 11 games between the pair.
That statistic rankles but Wenger’s sides have also suffered from sendings off for petulance.
Striker Olivier Giroud earned two yellow cards for dissent and a bad tackle on Wednesday during Arsenal’s 2-1 defeat by Dynamo Zagreb in the Champions League.
(Reporting by Clare Lovell, editing by Mike Collett)