After the match Henman told of his disappointment but was optimistic about the future.
Murray's sensational climb up the rankings coincides with long-time British number One Henman's slide.
Henman has a 6-6 record against Federer but has lost their last five meetings.
Henman then reeled off four successive points from 40-15 down to move 4-1 up.
But as the fans pondered the possibility of a Henman fightback, Federer assumed total control.
Defeat was a blow to Henman's hopes of qualifying for the end-of-season Masters Cup.
British number one Tim Henman has already given his cautious backing after initially opposing the idea.
Despite the defeat Tim Henman retains eighth place in the latest ATP world rankings.
"I'm frustrated with the outcome, obviously, and somewhat disappointed with my performance, " Henman said.
Annacone, who used to coach Pete Sampras, has been working with Henman since December 2003.
Henman has tumbled to 28th, with British number two Greg Rusedski just a spot behind in 29th.
But if those are his sentiments, you can probably multiply that feeling by 10 times for Henman.
Henman will be part of the BBC's commentary team for Wimbledon 2010, which begins on 21 June.
Fish beat Tim Henman and Tommy Robredo at the Madrid Masters last week before losing to Roger Federer.
But her act of defiance against the inevitable summed up Henman's display, starting well but fading pretty quickly.
Bogdanovic will meet the winner of the match between Andy Murray and Tim Henman which takes place on Wednesday.
Henman never looked back, breaking in the sixth game of the second set to again gain the upper hand.
Henman broke again in the eighth game to take the first set 6-2.
Despite some inspired play by Henman, Sampras showed cool consistency to keep his challenge for a fifth title alive.
Henman, seeded three, then held his serve comfortably thanks to four serve-and-volley winners to take a clear 5-3 lead.
"Federer could beat anyone, " said Don Coop after Henman lost the second set.
Great Britain's main weakness has always been an over-reliance on Henman and Rusedski.
The first set was over in just 26 minutes as Henman broke Black in the fourth and sixth games.
The 19-year-old broke twice to Henman's once to claim the first set 6-4.
Lee briefly rallied in the third set, but never looked likely to be able to force Henman into a fourth.
Henman broke in the opening game and raced into a 3-0 lead before Lee, the British number three, had settled.
Henman reached set point from another mistake, but misjudged a defensive lob and missed on his spinning return, going wide.
One possibility is that Henman might play a smaller part and allow a chance in the reverse singles against Udomchoke.
Murray is aiming to join compatriot Tim Henman in the second round after the other four Britons all went out.
And with Greg Rusedski also struggling with fitness, Henman will be expected to prove his commitment to the British cause.
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