In a highly-charged first round clash at Roland Garros, world number two Sabalenka won 10 of the last 12 games to sail to a 6-3, 6-2 victory.
However, in a match where the build-up had been overshadowed by the continuing sporting fallout from Russia's invasion of Ukraine, Kostyuk followed through on her promise not to shake hands with Sabalenka. Belarus is a key military ally of Moscow.
The Ukrainian was widely jeered as she packed her bags and left Court Philippe Chatrier.
Sabalenka insisted that all Belarusian and Russian players are opposed to the war which has raged on since February 2022.
"Nobody in this world, Russian athletes or Belarusian athletes, supports the war. Nobody," she said. "If we could stop it, we would do it."
However, Kostyuk, one of the most vociferous opponents of the continued presence of Russian and Belarusian players in the sport, hit back.
"She never says that she personally doesn't support this war, and I feel like journalists should change the questions that you ask these athletes because the war is already there," she said.
"I feel like you should ask these players who would they want to win the war because if you ask this question, I'm not so sure these people will say that they want Ukraine to win."
Sabalenka can become the new world number one after the French Open and Kostyuk believes the Australian Open champion will then have a global platform from which to denounce the war.
"There are so many platforms that millions, billions of people in the world read. And just to reject her responsibility of having an opinion on the most important things in the world, I cannot respect it," said Kostyuk.
'People should be embarrassed'
"She said that I hate her. I never said publicly nor privately nor to anyone that I hate Aryna Sabalenka or any of the players. I just don't respect her because of her position in this situation."
She added: "I personally know athletes from tennis who support the war. To say nobody does is a little bit strong."
Sabalenka said she sympathised with Kostyuk being subject to jeers from the French crowd.
"I understand why they are not shaking hands with us. I can imagine if they gonna shake hands with us, and then what's gonna happen to them from Ukrainian side? So I understand that," said Sabalenka.
"And I understand that this is not kind of like personally. I think she don't deserve to leave the court that way."
Kostyuk questioned the crowd's motives in booing her stance.
"I want to see people react to it in 10 years when the war is over. I think they will not feel really nice about what they did," she said.
"I didn't expect it. People should be honestly embarrassed."
Sabalenka initially thought the boos were targeted at her rather than Kostyuk.
"They saw it as disrespect, so that's why it was booing to her. But at first I thought they were booing me. I was a little confused, and I was, like, 'Okay, what should I do?'," said Sabalenka who had performed an exaggerated and theatrical bow at the end of the match.
Kostyuk was last in her home city of Kyiv in March where her father and grandfather still live. She is currently based in Monaco, living with her mother and sister.
The war is never far away for Kostyuk. On Saturday night, Kyiv saw the largest drone attack since the beginning of the Russian invasion. The attack killed two people and wounded three others.
Kostyuk famously refused to shake hands with Sabalenka's Belarusian compatriot and former world number one Victoria Azarenka at the US Open last year. She opted instead for a cursory touch of racquets at the net.
Since then, it has become a common sight with Ukraine's Elina Svitolina refusing to shake hands with Russian Anna Blinkova after winning the Strasbourg final on Saturday.
