While the inquest into the Premier League champions' dismal campaign will continue long after their 2-0 quarter-final reverse at Everton, the immediate topic consuming social media centred on the combustible Spain striker's sending-off, surprisingly his first for Chelsea.
Alan Shearer, one of England's greatest strikers, joined the debate by telling BBC viewers the Brazilian-born forward had become "tiresome".
Much of the attention focussed on whether Costa, who became embroiled in a late face-to-face brouhaha with Everton's Gareth Barry, had gone as far as biting his opponent, Luis Suarez-style.
Another question was whether he spat at the feet of referee Michael Oliver after being booked earlier for an altercation with Barry.
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"It's tiresome from him now. He spends too much time abusing and fighting and scrapping," Shearer said. "You can't do that every game because you turn the ref against you."
This has been a regular debate surrounding Costa in a season which, for the first time since Roman Abramovich became owner in 2003, has effectively ended for Chelsea in March.
Despite his improvement in form after a disinterested start to the campaign under previous manager Jose Mourinho, Costa still often becomes involved in off-the-ball wars that overshadow his hit-or-miss contributions in front of goal.
GRANDFATHER CLOCK
Here was the ultimate example. After being fouled by Barry, who was happy to wind Costa up like an old grandfather clock, the Spanish international jumped up for a tete-a-tete and ended by burying his head into the Everton midfielder's neck.
It looked momentarily as if he was opening his mouth to bite Barry but there was absolutely no reaction from the England man to suggest he had, and it all ended with Costa offering an unconvincing embrace.
Oliver, though, had seen enough of Costa's antics to send him off for a second yellow card in the 84th minute and his tormentor Barry was similarly dismissed soon after for a foul on Cesc Fabregas.
Everton manager Roberto Martinez told reporters: "Gareth said it's nothing to be worried about ... Diego Costa has a fighting spirit. I don't think it was much.
"Whatever happens with Costa I think we should see it as what we want to see in a cup game, real emotions."
Chelsea manager Guus Hiddink said: "I didn't (see the incident) and everyone who follows me knows I try to be fair in my judgement whether it's pro or con.
"I don't want to give a judgement in this but he (Costa) was chased a bit in the game as well. They knew it."
(Reporting by Ian Chadband; Editing by Tony Jimenez)
