The Spain international was sent off for his first time in his Blues career with two yellow cards in the 2-0 Toffees win, but hit the back pages for his supposed bite on Gareth Barry.
Barry later insisted Costa had not bitten him, meaning he had no case to answer for neither that incident or claims he made an inappropriate gesture to Everton fans.
However, he was given an automatic two-match ban for his sending off and now he will miss out on a further game for his behaviour towards the referee, as he protested his dismissal and refused to leave the pitch.
Costa has also been fined £20,000 and warned over his future conduct, the Football Association has announced.
His initial suspension ruled him out of the draw with West Ham and Saturday’s Premier League clash with Aston Villa, and now he will also miss the April 9 match at Swansea.
An FA statement read: “Following an independent regulatory commission hearing on Thursday (March 31, 2016), Chelsea’s Diego Costa has been given a one-match suspension, fined £20,000 and warned as to his future conduct.
“The forward admitted a charge of improper conduct in relation to his behaviour after he was shown a second yellow card in the FA Cup sixth-round tie on March 12, 2016 at Goodison Park.
“This suspension will follow immediately on the conclusion of the player’s current ban.
Costa has scored 11 goals in his last 16 games for Chelsea under Guus Hiddink. The interim boss admitted on Friday he would use the final eight games of the Premier League season to “experiment”.
With Costa suspended, Eden Hazard (groin/hip) injured and Oscar, Willian and Bertrand Traore only rejoining Chelsea on Friday following international duty, Alexandre Pato could make his long-awaited debut in Saturday’s lunchtime kick-off at Villa Park.
“We now have eight games coming up, and there’s not much to win for Chelsea anymore. There might be some time for experiments,” Hiddink said.