The Spain striker appeared to tread down on Emre Can and Martin Skrtel in the second leg clash at Stamford Bridge, that Chelsea won 1-0 to book a place in the Wembley final.
The west London club will be waiting anxiously to see if the Football Association choose to take retrospective action.
Any suspension could rule Costa out of Chelsea's crucial top-of-the-table Premier League clash at home to second-placed Manchester City, who they lead by five points, on Saturday.
Liverpool manager Brendan Rodgers had little doubt the Brazilian-born striker should have been sent off.
"There’s no need to do it. He’s a top class player. He knows how to do it so the officials don’t see. It wasn’t good for the game. It’s disappointing to see such a good player behave like that," Rodgers told reporters.
Chelsea manager Jose Mourinho saw things differently.
The Portuguese, no stranger to conspiracy theories, sought to explain away the incidents as nothing more than accidents blown out of proportion by TV pundits.
"I don’t know what you understand by stamp. I think you are already influenced by -- there is a campaign by a certain pundit that talks about Diego Costa's crimes," he told reporters after former Liverpool midfielder Jamie Redknapp analysed the match.
"What (broadcaster) Sky calls crime, it’s absolutely accidental.
"When you are there and you are paid and you are very well paid -- these guys they have a very good seat, they are always right and they always win but they should be honest."
COMBATIVE APPROACH
Costa has taken to English football like a duck to water, with his combative approach suiting the high-tempo physicality of the Premier League.
The striker has scored 17 league goals since arriving from Atletico Madrid in the close season.
He was a handful for Liverpool's defenders all evening and was unfortunate not to win a penalty in the first half when he was felled by a clumsy tackle from Slovakia defender Skrtel.
Chelsea's winner arrived four minutes into extra time when Branislav Ivanovic rose unmarked to power home a header from close range to send them to the March 1 final.
The defender was singled out for praise by Mourinho, with a "bloody boot" evidence of the Serb's commitment to the cause.
"I think Ivanovic’s boot should go direct to the academy for the kids to see all the blood," Mourinho said.
"The boot is a white boot but it’s completely red. He had a big cut -- he gave absolutely everything."
(Writing by Toby Davis; additional reporting by Clare Lovell; editing by Ken Ferris)
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