Some booing and jeering could be heard after the match as Kostyuk refused to shake hands with her opponent, having said beforehand that she would not do so with Russian and Belarusian players due to Moscow's invasion of its neighbour.
Sabalenka, who appeared to sarcastically bow to the crowd following the win, said she initially thought the boos were aimed at her.
"It was a very tough match, I mean tough emotionally. I'm sorry guys, I didn't get it at first, I thought this booing was against me so I was a little surprised," she said.
"But then I felt your support, so thank you so much."
The world number two has previously said she has nothing against Ukrainian people and felt bad for them as Moscow's invasion rages on. Belarus has been a staging ground for Russia's actions.
Sabalenka appeared to be in a spot of bother on serve early on and fell behind 2-3, but the unseeded Kostyuk could not build on her advantage and the Australian Open champion struck back immediately with a powerful crosscourt volley on breakpoint.
Second seed Sabalenka wrapped up the first set in style in front of a sparse Court Philippe Chatrier crowd before pouncing in the next with an early break and another to go up 4-1, as Kostyuk wilted under the Paris sun.
The Belarusian raised her level again late in the match to save two breakpoints and close out the victory in 71 minutes.
Kostyuk did not deserve jeers, says Sabalenka
Sabalenka said she understood Kostyuk's decision to skip customary post-match handshakes with Russian and Belarusian players following Moscow's invasion of her country Ukraine but the player did not deserve jeers from the French Open crowd.
"I understand why they're not shaking hands with us. I can imagine if they shake hands with us, what's going to happen to them from the Ukrainian side. I understand that this isn't personal. That's it," Sabalenka said.
"I think she didn't deserve to leave the court that way."
Sabalenka said Russian and Belarusian athletes did not support the war.
"How can we support the war? Nobody, normal people will never support it," Sabalenka added.
"Why do we have to go loud and say that? If it could affect anyhow the war, if it could like stop it, we would do it. But unfortunately, it's not in our hands."
Kostyuk said the section of fans who jeered her might feel differently in the future, adding she did not expect to face a similar situation at Wimbledon where the next Grand Slam will take place in July.
"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," Kostyuk said.
"Wimbledon banned them (Russian and Belarusian players) last year and when I was in the UK last year, people were reacting to us differently even on the street. I felt a lot of support.
"I'm pretty sure the reaction would be different."
