Former Arsenal chairman Peter Hill-Wood hit out at the Spain international after Per Mertesacker saw red for a foul on the striker, leaving the Gunners down to 10 men after just 18 minutes.
Costa then went on to score the winning goal as Arsenal slumped to yet another defeat to Chelsea but Hill-Wood could not contain his anger after the loss.
“He is a serial cheat and he gets away with it,” Hill-Wood told the Daily Star. “I think he deliberately ran in front of Mertesacker, who hardly touched him.
“Yet Costa rolls around as if his legs have been cut off. Once the red card’s been shown, he’s suddenly perfectly alright again.
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“Personally I think the referee should have sent him off for diving. It’s very annoying because to me it is blatant.”
Manager Arsene Wenger claimed after the game that Costa had got Mertesacker sent off and Hill-Wood claimed the Frenchman was also enraged by the Chelsea forward.
“I thought Arsene was very restrained because he must have been furious,” he added.
“He gets criticised or penalised by the FA if he says too much.”