Kokkinakis bowed out with a 6-4 6-1 3-6 7-6 (7-5) third-round loss to Russian 11th seed Karen Khachanov at Roland Garros on Friday.
Kokkinakis fought gamely to extend the match to almost five sets after engaging in a running verbal battle with chair umpire Katarzyna Radwan-Cho.
At one point, Kokkinakis was left exasperated at being denied the chance to go for a toilet break after losing the second set.
"All I'm asking is to try and piss," he pleaded to the official.
"I get two for a match. Do you want me to piss on the court? Is that what you want? So what do you want now?
"I'm asking to go to the toilet. I like cramped in my last match cos I couldn't .. so brutal."
Despite the drama, Kokkinakis battled back to take the third set, then have the world No.11 on tilt in the fourth.
Khachanov has reached the last four at the past two grand slams after ousting Kokkinakis's doubles partner Nick Kyrgios from last year's US Open quarter-finals.
But he looked a beaten man when Kokkinakis served for the fourth set, then forged to a 4-1 lead in the fourth-set tiebreaker.
Alas, Australia's last man standing in Paris once again fell in the third round after surrendering his big fourth-set lead.
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