The world number 20 did not shake hands with top-ranked Belarusian Aryna Sabalenka after being beaten in Sunday's final in straight sets.
Like many Ukrainian players, Kostyuk refuses to shake hands with Russians or Belarusians following Moscow's invasion of her homeland.
In her speech at the trophy presentation, the 23-year-old Kostyuk said: "I want to say a few words about Ukraine.
"I play every day with a pain in my heart, and there are thousands of people who are without light and warm water right now.
"It's minus 20 degrees outside, and it's very painful to live this reality every day," she said, her voice cracking with emotion.
Post-final ceremonies usually involve players congratulating their opponents.
Kostyuk did, however, thank "all the opponents I've played this week."
Sabalenka, who has said in the past that she does not support the war, congratulated Kostyuk on reaching the final in her on-court speech.
Writing on Instagram, where some users accused Kostyuk of poor sportsmanship, she wrote: "The words I shared after the match sparked a lot of reaction.
"For me, it's a conscious choice to keep reminding people of what Ukraine and its citizens are going through.
"Thank you to everyone who showed support. And thank you to all the players I faced on the other side of the net this week."
Both players will be at the Australian Open starting on Sunday, where Sabalenka is the favourite to win the title for the third time in four years.