But he did not fool referee Michael Oliver who presented him with a second yellow - and a subsequent red card - in the 84th minute.
He received his first yellow card in the 11th minute of the match for a foul on Barry, who he later appeared to bite.
In April 2013, ex-Liverpool footballer Luis Suarez was given a ten game ban after biting a Chelsea player.
During a 2-2 draw at Anfield, Liverpool, the Uruguayan striker bit Branislav Ivanovic - the second time he had taken a chunk out of a rival player in his career.
Chelsea were already losing 2-0, with their former player Romelu Lukaku scoring both goals, when Costa was sent off.
Barry played down the incident after the match and said it was 'nothing to worry about', his manager Roberto Martinez said.
The west London team crashed out of the FA Cup just days after being knocked out of the Champion's league also.
Costa was already facing potential punishment after he appeared to make a rude gesture towards Everton fans at Goodison Park, Merseyside, as he went into the locker room at half time.
With the scores tied at 0-0, the Spaniard was seen 'giving two fingers' to the home fans as he walked off the pitch.
A number of social media users also accused the striker of spitting at the feet of Mr Oliver after he showed him a red card.
Since signing for Chelsea for a reported £32million in 2014, Costa has been involved in a string of controversies, receiving a number of violent conduct charges from the English Football Association.
In January 2015, he was given a three match ban for stamping on a Liverpool player. The rival team's manager later said Costa 'could easily have hurdled over the player'.
He was given another three match suspension after clashing with Arsenal defender Laurent Koscielny in November.
In the same month, he launched a bib at then Chelsea manager Jose Mourinho after being named substitute for their match against London rivals Tottenham.
Today's FA Cup match represented Chelsea's last chance to win silverware this term after they were dumped out of the Champions League by PSG.
Their defence of their Premier League title was undone by a poor start to the campaign.
Costa is also facing suggestions from a number of Twitter users that he spat at the feet of referee Michael Oliver after his decision to give him a yellow card.
-DAILY MAIL
