Barry confirmed he was not bitten by Costa as the controversial Chelsea player found himself at the centre of a fresh storm.
Television cameras focused on Costa nuzzling his mouth into Barry's neck six minutes from time, and it looked as if the Spain striker was prepared to bite him.
Costa appeared to think better of it, though he was still dismissed for a second bookable offence after grappling with the England international.
"Seen a lot of talk about the incident between me and Diego Costa in the game last night," Barry said on the Fanzai App website.
"For the record, Diego did not bite me."
The Football Association is awaiting referee Michael Oliver's report before making a judgement on Costa's latest misdemeanour, but Barry's comments will certainly help his case that nothing untoward took place.
Costa will, however, definitely receive an automatic one-match ban for his sending-off - as will Barry, who followed him down the tunnel minutes later after collecting his own second yellow card in the game.
Barry will miss Everton's Barclays Premier League home game against Arsenal on Saturday, while Costa will sit out West Ham's visit to Stamford Bridge on the same day.
Chelsea boss Guus Hiddink, who said his player had been "chased" during the game, later joked that he and Costa should go together to watch the film "Anger Management" after a catalogue of incidents since his £32million arrival at Stamford Bridge during the summer of 2014.
Costa is no stranger to controversy and had collected his 10th Chelsea yellow card of the season before seeing red.
But his dismissal was actually the first of his Chelsea career and Joey Barton, another player who has had his brushes with officialdom down the years, called for a measured response to the Spaniard's actions.
"I have been involved in numerous incidents, similar if not worse, on a football pitch - tempers get frayed, that's football," Barton told BBC Radio Five Live's Sportsweek's programme.
"We wouldn't want players to be walking round cold and calculated and emotionless because we wouldn't be getting the product that we all love.
"I'm not saying we accept it - there are many things I've done which aren't great for the game and if you could go back and change them, you would.
"But strange things happen to people when they have got adrenaline and emotions coursing through their veins during football matches, during any sport, really.
"You are better working with what he's got because the reality of it is Diego Costa is, from time to time, a pantomime villain, but he's a fantastic footballer."
Source : PA
Source: PA