Costa was dismissed for a second bookable offence six minutes from the end of his side's 2-0 FA Cup quarter-final defeat at Goodison Park after an ugly clash with Barry during which he appeared to make a motion to bite the Toffees midfielder before thinking better of it.
Barry did not speak to the media after the game, but Press Association Sport has been told he has privately dismissed the allegation, which was also denied by Costa in a club statement late on Saturday night.
The Football Association is awaiting referee Michael Oliver's report before making a judgement on the Spain international's latest misdemeanour, although Barry's evidence could prove invaluable to him.
However, Burnley midfielder Joey Barton, himself no stranger to the game's disciplinary chiefs, has urged the football authorities not to overreact to "pantomime villain" Costa's most recent rush of blood.
Barton told BBC Radio Five Live's Sportsweek's programme: "It's difficult to get too self-righteous when you're in my position, but what we have to remember is nobody has died.
"It's a game of football
You have had two grown men basically square up, no punches have been thrown, nothing serious has happened, both have gone home to their families, one team has lost, one team has won.
"We have to be careful not to get too carried away
We have to remember what makes football football
It's that kind of thing, it's goals, it's playing on the edge, it's high intensity, it's high passion
That's why we do what we do, that's why we love watching football."
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.
But Barton again called for a measured response, stating that passion and emotion were vital components of the game.
He said: "I have been involved in numerous incidents, similar if not worse, on a football pitch - tempers get frayed, that's football
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 see lots of instances in sport where it happens because we care.
"I know that's not an excuse, but I don't think you want to take the edge off him
If you take the edge off him or players who play like that, it's very rare that they end up becoming better for it.
"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