Bryant took up tennis following his retirement and was friends with a number of leading players.
He was at the US Open last summer and sat in Naomi Osaka's box for one of her matches.
He also wrote a children's book about tennis released last year called Legacy and the Queen.
Kyrgios looked close to tears as he walked out for his fourth-round clash with Rafael Nadal wearing a Los Angeles Lakers jersey bearing Bryant's original number eight.
The Australian said: "I never met Kobe. But basketball is practically my life. I watch it every day. I've been following it for as long as I can remember.
"When I woke up to the news, it was pretty emotional. It was pretty heavy all day.
"It's just tough. It's horrible news."
Kyrgios lost in four close sets, recovering from a break down in the fourth to force a tie-break.
The 24-year-old said: "If you look at the things he stood for, what he wanted to be remembered by, I felt like, if anything, it helped me tonight.
"When I was down a break in the fourth, I was definitely thinking about it. I fought back."
Nadal had an association with Bryant through Spanish basketball star Pau Gasol, Bryant's former Lakers team-mate.
The world number one said: "He (Gasol) always told me he is a spirit of hard work, he always wanted to increase his level. He is a true inspiration for the world of sport and for a lot of kids.
"This is one of those days you want to forget but of course Kobe Bryant will be in our hearts and in our minds for the rest of our lives."
Coco Gauff, who Bryant had spoken glowingly about at the US Open, paid her own tribute, writing 'Mamba Mentality' and number eight on her shoes for her women's doubles match.
A montage of Bryant in action was played on the big screen in Rod Laver Arena ahead of Kyrgios' clash with Nadal.