Henman was less than impressive against the world No 350 and his performance was further marred when he was warned for uttering a "verbal obscenity" after shouting at a fidgety cameraman at courtside. His subsequent outburst betrayed his disgust at failing to win the fourth set and with it the match.
Henman said: "I expressed my feelings at my performance to the referee and probably deserved the warning, but I won't lose much sleep over it.
"I was more concerned that I lacked the mental intensity at times to command the match against an opponent who played some good tennis. At least I stuck to my game plan which was to be aggressive - and got the job done in the end."
The tie is being played here on clay, a surface on which Britons have rarely performed well. Looking ahead to his second singles match tomorrow against Medvedev, the world No 17, Henman said: "It is Andrei's favourite surface here and it's going to be very tough, but hopefully I can produce an upset."
The prospect looks unlikely, though, on the alarming evidence of Henman's erratic performance against an uncelebrated opponent in yesterday's game.
Rybalko stretched the Briton to the limit with a giant-killer fervour and plucky spirit that was stirred up by a vociferous home crowd, determined to get their money's worth from tickets costing the equivalent of pounds 55, nearly half the country's average monthly wage.
Henman, still officially the world's 20th best player, eventually prevailed 3-6, 6-4, 6-3, 4-6, 6-4 in just over three testing hours. Although he played a number of splendid passing shots, his games was also littered with unforced errors and missed first serves.
"Apart from the win, which is the most important thing, I didn't get much satisfaction from this performance," Henman said. "It was very average."
He knows he must come up with a much higher level of consistency and drive against Medvedev, who is the hero of Kiev and appears to be back to something near to his most compelling form after a few years in the doldrums following knee and wrist surgery.
Medvedev looked razor sharp as he beat Rusedski 6-1, 6-1, 2-6, 6-2. The Briton, playing in the country of his grandfather's birth, was overwhelmed in the first two sets, but fought back bravely to take the third.
Medvedev suddenly looked concerned, but the reprieve for the British contingent was only brief as he took an early break for a 3-1 lead in the fourth. The Ukrainian still had to survive a spate of double faults to resist Rusedski's continued brave efforts, but eventually took command again to clinch victory in just over an hour and a half.
Today's doubles will see Henman and his Olympic Games silver medal partner, Neil Broad, face Medvedev and Dmitri Poliakov.
DAVIS CUP (Kiev): Ukraine and Britain level at 1-1 (Ukraine names first): A Rybalko lost to T Henman 3-6, 6-4, 6-3, 4-6, 6-4; A Medvedev bt G Rusedski 6-1, 6-1, 2-6, 6-2.
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