Bent had been in coach Fabio Capello's 30-strong squad before the Italian dropped the Sunderland forward and six other players on Tuesday.
Bent netted 25 goals for Sunderland last season but did not score in either of his starts for England, against Brazil in November and Japan on Sunday.
Bent lost out to Aston Villa striker Emile Heskey in a cull of the squad which also meant Theo Walcott, Tom Huddlestone, Scott Parker, Adam Johnson, Michael Dawson and Leighton Baines would not be flying out to South Africa later on Wednesday.
Bent told his club's website: "I feel really disappointed. I have always said to myself, if you play well and do your best for Sunderland, then there is a chance you can go to the biggest tournament in the world. But obviously on this occasion it has not worked out.
"Straight away from when Mr Capello spoke to me and told me I wouldn't be involved in the 23-man squad my thoughts turned to next season and how I can improve on what I have done for Sunderland this year.
"I am going to take some time off now and rest my bones after what has been a great season for me and get ready for next year. It's a case of fully concentrating on my football for Sunderland and doing my best for them.
"Of course, I still want the boys to do well. I have got a lot of friends in the England set-up. They are a great bunch of lads and, even though I won't be there, I will be supporting them."