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The six-times world finalist – runner-up in 1984, 1990, 1991, 1992, 1993 and 1994 – last played at the Crucible Theatre in 2006, but has not given up hope of returning to the sport's biggest stage by coming through four qualifying rounds.
"He potted some really good balls," said White, who has been battling the eye inflammation of conjunctivitis. "In the first frame, I missed an easy ball on 38 when I should have got a big break. I won the first frame on the colours, but I didn't really settle.
Watch Jimmy White beat Ivan Kakovskii in World Championship qualifier
"My focus was in and out. I was expecting great things, but it didn't happen. I've been practising hard and producing good stuff, but when you come to a tournament you want to win so bad and make so many unforced errors, it's mind-blowing sometimes.
"But that's why the game is so exciting. I've got a bit of conjunctivitis and I think that's because I'm revved up and ready to go."
White's 21-year-old opponent was not even born when he lost 18-17 to Stephen Hendry in his last world final appearance 26 years ago, but he still had too much for his young rival at the English Institute of Sport.
Kakovskii made a break of 60 to level at 1-1 and a 76 to close to 4-3 behind, but the 1992 UK champion finished strongly with runs of 54 and 58 seeing him progress to a match with former Shoot-Out champion Michael Georgiou on Thursday afternoon.
"From 4-2 up, I stole a couple of frames, but when it went 4-3 I felt okay then and it is nice to know I have it in the armoury when I'm under pressure to feel okay," added White.
"I've got to stay focused against Michael and can't get too ahead of myself. Everybody wants to get to the World Championship and show your class over the longer distance."