Graham is adamant the Spain striker should have been sent off for bumping the chest of Laurent Koscielny and raising his hands to the Frenchman's face in the first half at Stamford Bridge, before Gunners defender Gabriel saw red for retaliation.
Although Costa got away with only a yellow card, Graham says referees are now likely to seek to ensure he does not escape stricter punishment in future.
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Graham told BBC Radio Five Live's Sportsweek: "I think [Costa] is going to be targeted man now by the officials and probably rightly so.
"[Didier] Drogba was the main man [at Chelsea] for nearly 10 years and he was very, very physical, but he didn't take to the extremes that Costa has taken it to.
"Although you've got to keep that physical intensity, once you step over the mark he's got to be dealt with by officials, it's as simple as that - and I think he will be."
But Graham also suggested Arsenal manager Arsene Wenger ought to be stricter with his own players, with Santi Cazorla's second-half dismissal taking the number of Gunners players dismissed in the Premier League to 79.
Graham added: "[Wenger] is not the most strict manager and he really needs to get hold of his own players because there's no way [Gabriel] should have been sent off - it's his own stupidity that got him sent off and they've got to handle that.
"[But] Arsene does it his way and look at the record he has got in English football.
"He has been instrumental in getting a certain way of playing - he's brought all these things and trophies as well so how can you fault him?"