Manager Roberto Martinez claims the midfielder says it is nothing to worry about.
The two players clashed on several occasions in a heated FA Cup quarter final on Saturday evening, in a game which Barry’s Everton side eventually won.
It was conflict towards the end of the game that courted the most controversy though as Costa reacted angrily to a foul by Barry with many claiming he had bitten the veteran midfielder.
The footage of the incident so far has been inconclusive and Everton manager Roberto Martinez says his midfielder has played down the incident.
“Gareth Barry said 'It's nothing to be worried about, I'm just disappointed to get a second yellow card'," the Mirror reports Martinez as saying.
"It is a game full of emotions and there were two sending-offs, the referee played a very good game."
While Barry has played down the incident, it is sure to be one that the FA will be keen to analyse further.
Costa will already be serving a ban after picking up a red card, his first at Chelsea, and if he is found guilty of biting he is sure to face even more time on the sidelines.
Luis Suarez was handed a four-month ban by FIFA for biting Italy defender Giorgio Chiellini and Costa would likely face a similar one now given that precedent has been set.