"I think I was struggling a little bit with the timing in some of the points and just trying to find my rhythm", she said.
Her Open victory - the second title of her career with the first coming at Indian Wells in April - was marred by controversy as opponent Serena Williams initiated a number of run-ins with umpire Carlos Ramos during the match.
"It's very nice to be back in Singapore and I'm very, very happy with the match tonight, with the performance tonight", Svitolina told the crowd.
Osaka has fond memories of the Singapore venue hosting the WTA Finals for a fifth and final time next week, where she will return to an arena three years after she won the Rising Stars Invitational tournament on the same Indoor Stadium court.
White Group: 2-Caroline Wozniacki; 4-Petra Kvitova; 6-Elina Svitolina and 7-Karolina Pliskova.
Caroline Wozniacki squandered break points in the eighth and 10th games in a disappointing start to her title defence.
"I'm really sure it's not our last final, and see you in Maldives or somewhere".
"You have to play your best level because everybody is very strong playing here". "From the beginning you have tough matches and even if you don't start well, you are still alive and fighting for a semi-final spot", Svitolina added.
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After she returned to the stage, Svitolina said she hoped to recover in time for what she expected to be another tough match.
Kasatkina got the decisive break in the eighth game to lead 5-3 but nerves hit her the next game and Jabeur miraculously broke serve despite clutching at her left thigh in pain as cramps started to take over. Six of her seven double-faults came in the first set.
"I think there were times where I played really well, and I was trying to move her around, but there were also times when I just didn't time the ball perfectly". She won their first meeting in the 2016 Acapulco quarterfinals in straight sets.
Svitolina set up the second-set win by breaking Kvitova's serve to go ahead 4-2. This is what sport is about and I really appreciate that we had this match today and I wish you all the best and good luck.
"I remember past year we played a lot".
Battling back and forth with Romanian great Simona Halep for much of the 2018 WTA Tour, Wozniacki now emerges as one of the top contenders for the title in Singapore.
"I think with someone like Petra, she can play maybe not as well in one match and extremely well in the next".
Osaka has been drawn in the Red Group of the eight-woman event alongside Angelique Kerber, Kiki Bertens and Sloane Stephens, her predecessor as U.S. Open champion who she takes on first in round robin play on Monday.