Costa clashed with both Arsenal centre-backs late in the second half, twice lashing out at Laurent Koscielny with his hand and then exchanging words with Gabriel.
After Costa and Gabriel were both booked, the Arsenal man was sent off for kicking out at the Chelsea striker, but Wenger felt that Costa should have been sent off for his role as instigator.
?I would not like to be Mike Dean tonight,? Wenger told BT Sport. ?Costa twice should be sent off. He hits him (Koscielny) in the face on purpose.
?In every game he has aggravation and he gets away with it because of the weakness of the referee.
?We knew before the game he is only looking at that. Gabriel should not have responded at all, but the two sending-offs for us and Costa staying on the pitch is a shame.?
Chelsea manager Jose Mourinho refused to be drawn on Gabriel?s dismissal, but praised Costa for his performance.
?I don?t have a view on the sending off,? said the Portuguese. ?Man of the match for sure was Diego Costa. He brought everything to the game.?
Arsenal finished the match with nine men after Santi Cazorla was shown a second yellow card for sliding in on Cesc Fabregas in the 78th minute.
Kurt Zouma headed Chelsea in front from Fabregas?s free-kick early in the second half and Eden Hazard added a second goal with a deflected shot in the 89th minute.
The result gave Chelsea, the defending Premier League champions, a first home win of the campaign, after a return of four points from five games that represented their worst start to a league season in 29 years.
?It was a good victory. We need to win matches,? added Mourinho, whose side opened their Champions League campaign with a 4-0 home win over Maccabi Tel Aviv on Wednesday.
?We won twice in three days, we kept two clean sheets. We controlled the matches.?