The Argentine midfielder retweeted a post calling for the pair to leave Los Che only to remove it almost immediately after allegedly realising his error.
However, Costa's apparent support of the cause was picked up by several fans and he was forced to issue a swift explanation for his actions on the social networking site.
"There has been an error on my twitter ... Never in my life would I support something like this!! I do not go along with this, that's for sure ..."
Costa opened the scoring in Valencia's 2-2 draw with Mallorca at Mestalla on Sunday evening only to be later dismissed for a lunge on Alejandro Alfaro.
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