The Reds were defeated 2-0 away from home in the Champions League.
Serbian international Markovic was liking tweets that had Serbian flags and hearts in them.
And Liverpool fans were not pleased.
One fan wrote on Twitter: "Just leave Lazar it's for the best."
Another said: "How is Markovic that t**t liking this?
"I honestly hope this guy is released by us in January because he simply doesn't deserve to be here anymore."
Markovic has not been included in the first-team squad this season after a move to Anderlecht in the summer fell through.