The Blues were dumped out of the competition after a 2-2 draw, with PSG advancing to the quarter-finals of the Champions League by virtue of the away goals rule.
Costa was in the mood to get something off his chest and tried to confront Cabaye after the final whistle was blown.
Wearing a puffer jacket, Cabaye angrily shouted at Costa although it is unclear what acted as the catalyst for the argument.
Costa was eventually shepherded off the pitch as PSG officials and a Chelsea steward intervened.
ACTION
Diego Costa shouts at Yohan Cabaye after the final whistle
When I got the red card all the Chelsea players come around. It felt like I had a lot of babies around me
Zlatan Ibrahimovic
The Spaniard was involved in a number of feisty battles during the game including a skirmish with Thiago Motta.
Jose Mourinho at one point had to tell Costa to calm down.
And Zlatan Ibrahimovic stuck the boot in after the game, labelling the Chelsea players 'babies' after he was sent off.
He said: "That is not the worst. The worst is when I got the red card all the Chelsea players come around. It felt like I had a lot of babies around me."
DIGITAL SOUTH
Yohan Cabaye turns away as Diego Costa vents his spleen
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