He strained the muscle in training on 14 November and suffered a recurrence in Monday's straight-sets defeat by David Ferrer at London's O2 Arena.
"I was told to take a week to 10 days completely off - I just didn't have enough time to recover," said the visibly dejected Scot.
"I was probably going to do myself more damage playing than not."
Murray was scheduled to practise at 1300 GMT on Tuesday for an hour ahead of Wednesday's Group A match against Tomas Berdych.
But he failed to appear and a hastily arranged press conference was called at which the 24-year-old delivered news of his withdrawal.
He has been replaced by world number nine Janko Tipsarevic of Serbia.
"When I came off the court [on Monday], I was very disappointed and upset," said Murray.
"I said we'd see how I feel when I woke today up but I was never going to feel great. You hope things are going to get better, but in reality that wasn't ever going to happen.
"I woke up this morning still sore, came in and was going to hit. We chatted for about two hours - about when I was going to be practising, what I should do, what the right thing to do was.Continue reading the main story 19 - Andy Murray12 - Roger Federer9 - Rafael Nadal7 - Novak Djokovic
Matches played between end of US Open and start of ATP World Tour Finals
"I had some food, we spoke more about it. I was just trying to find reasons why I should try to play.
"But there was no real positive of coming out and playing because yesterday I was really unhappy on the court. I wasn't enjoying it at all.
"This is one of the best tournaments in the year, one that me and all of the players look forward to playing. I couldn't give anywhere near my best and that's what was disappointing."
After losing to Ferrer, Murray admitted that unless it was this event or a Grand Slam, he would not even have started the tournament.
He will now attempt to recover in time to begin his 2012 season at the Brisbane International on 1 January, with the Australian Open starting in Melbourne on 16 January.Continue reading the main story Wins: 56Losses: 13Titles: 5Australia Open: Finalist (lost to Novak Djokovic) French Open: Semi-finals (lost to Rafael Nadal)Wimbledon: Semi-finals (lost to Nadal)US Open: Semi-finals lost to Nadal)
"It might seem like it's a long time away but the Australian Open is six, seven weeks away," Murray continued. "I could mess up my preparation for that, for the beginning of the year.
"That off-season is so important for me in terms of getting myself in shape. It's one of the few times when you can have an actual training block.
"It's a strain - I definitely don't need an operation. It's not a major injury but it's something that I needed much more time than I had to get ready."
Murray added that he may have to think more carefully about his schedule in future.
Since the US Open, he has played more matches than any other member of the world's top four - Novak Djokovic, Rafael Nadal and Roger Federer - all of whom won their first matches at the O2.
"There's no chance I would have been ready to win the tournament here," Murray said. "In hindsight it was maybe the wrong decision [to play], but you also want to try and give yourself an opportunity, if you can.
"If you look at the other guys that played loads of matches this year, Roger and Novak both took a large break after the US Open. Rafa took one after Asia.
"Maybe me trying to get ready for Basel was too soon. That's something I probably need to learn from because I had played a lot of matches."