Henman, who will turn 33 next month, announced last week that he is to quit after Britain's Davis Cup world group playoff with Croatia at Wimbledon next month.
The Briton was beaten 7-6 2-6 7-5 6-4 by Jo-Wilfried Tsonga of France on Friday.
"I've got one more tournament - the Davis Cup, at Wimbledon, so a couple of nice wins there would be good," Henman told the crowd.
Though he admitted that he would have liked to have won Wimbledon, having reached the semi-finals four times, Henman said he had few regrets about his career.
"When I reflect on my career, I think I maximised my potential," he said. "This is as good as I could have been."
Henman reached the semi-finals at two of the other three grand slam events - the French Open and U.S. Open, both in 2004 - and reached a career-high ranking of fourth in 2002. He won 11 titles.
The back injury that had troubled him for the past three years flared up earlier this month when he arrived in the United States for the ATP event in Washington. Playing in pain, Henman said, was what convinced him to quit.
"I feel that with the level of tennis I've played and the things I've been able to achieve in tennis I didn't want to just keep plugging away and get the limited rewards I was going to get. That was the time when I sat down with (coach) Paul (Annacone) and knew that I wanted to stop.
"It's not something I actually planned, that Davis Cup was going to be my last event, but given the circumstances of it being at Wimbledon, it seemed to fit extremely well with me.
"It's always been an honour and a privilege to play any event at the All England Club so I'm really excited about playing there."
The closest Henman came to reaching a grand slam final came at Wimbledon in 2001, when he was two points away from beating Goran Ivanisevic in the fourth-set tiebreak of their semi-final, having led by two sets to one when the match was interrupted by rain.
"Yeah, if I could change one match, it would be that one, but if am asked do I want to go back and play Wimbledon? Really the simple answer is no.
"I played there so much over the years and have had some fantastic memories, some of the best memories of my career.
"But I've always felt like when I've been competing I've had the chance of winning any tournament, including Wimbledon.
"It's obviously getting more and more difficult to win it and I am not going to just hang around for the next nine months, just to play Wimbledon for the sake of it."
Henman, who has two young children with a third due next month, said the biggest thing he will miss is the competition, but said he expects to be involved in tennis at some stage in the not too distant future.
"That's the biggest upside, playing in stadium courts like this one (at Flushing Meadows). That's the final piece in the puzzle.
"In the short term I'm looking forward to stepping away from it but I don't envisage not being involved in tennis in the future."