Rusedski beat Sweden's Thomas Johansson 6-3, 4-6, 6-4 and said he was generally happy with his form but he was more keen to express his disappointment that he had been the last person to know about Henman's decision not to play in the World Team Championship in May.
"Tim talked to the press before I knew," he said. "I'm disappointed. This might have been the only chance for Britain to play there. It's also great preparation for the French Open.
"Last year he was asking me if I could play there and even trying to get a wild card [for Britain]."
Britain will not be eligible to compete in this year's team tournament in Dusseldorf because Henman has declared himself unavailable, preferring instead to take a week off to prepare for the French Open and the subsequent grass-court season in England.
Eight teams are selected for the annual competition using the combined rankings of each nation's top two representatives. Britain will not be chosen without Henman because their No 3, Andrew Richardson, is too far down the world list.
Rusedski won the opening set in 30 minutes with a stinging second serve of 134mph but Johansson, winner of back-to-back indoor titles last year in Copenhagen and St Petersburg, won the second set by breaking Rusedski's serve.
Rusedski earned a break for 4-3 in the third as Johansson saved one break point but double-faulted on the second to lose the game.
The Canadian-born naturalised Briton won through when Johansson sent a return long over the baseline.
Another quarter-final was taken care of without a match as Johansson's compatriot, Magnus Larsson, pulled out before his contest with the holder, Marc Rosset, of Sweden, with an ankle problem.
Britain's No 2, Lorna Woodroffe, reached the first singles final of her career at the WTA Challenger tournament at Redbridge Sports Centre, Essex, yesterday. The 21-year-old, seeded No 2, beat Tina Krizan, of Slovakia, 6-4, 6-4 in a semi-final lasting 73 minutes.
In today's final, Woodroffe, meets Yugoslavia's Sandra Nacuk, the world No 205 who beat Karen Cross, the third seed from Exeter, 6-3, 7-5 in 81 minutes.Reuse content