The club's English-language account posted a sarcastic message during the match questioning why the Brazilian forward had not been shown a second yellow card for what it called simulation, writing: "How many dives does it take to get a second yellow? Asking for a friend."
The post came after Vinícius went down appealing for a penalty in the Espanyol box.
Courtois addressed the message directly when speaking to reporters in the mixed zone after full time.
"I'd love to see all the tweets from the teams that play against us when they play other sides," the Belgian goalkeeper said, before turning his attention to another contentious incident from the game.
"As for them, Cala should have been sent off earlier."
The Real Madrid goalkeeper suggested Espanyol would do better to scrutinise their own players' conduct before criticising an opponent.
"First you have to look in the mirror and see your own players in the match," Courtois said.
He also pushed back more broadly on the idea that Vinícius' penalty appeal amounted to simulation.
"All forwards go down. It's very easy to look at your own side."
The exchange added an extra layer of needle to a game already notable for a heated post-match discussion around the treatment of Vinícius, with Jose Mourinho separately telling reporters that referees and opponents alike needed to do more to protect the winger from repeated rough treatment.
Espanyol boss Manolo González, for his part, defended his players when asked about Mourinho's comments, insisting none of the challenges on Vinícius during the match had been out of the ordinary.