"I certainly feel I could have contributed out there and have been working tirelessly to get into the best possible condition for the tour," Bell wrote on Twitter.
England selector James Whitaker said in an England Cricket Board (ECB) statement on Thursday: "Ian Bell has been an outstanding player for many years and undoubtedly still has plenty to offer England in the future.
"It was clearly a difficult decision but he has struggled for runs in recent series and we felt that it was the right time for him to take a break and spend time working on his game out of the spotlight."
Former England captain Kevin Pietersen took to Twitter to describe Bell's omission as "ridiculous" and "pathetic".
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"You have to take him for his experience," said Pietersen on a video hosted by www.breathesport.com.
"I do not get the thinking. Cook can go two years without a test hundred yet he plays every single game. It is pathetic. I think he has been hard done by here."
Batsmen Nick Compton and Gary Ballance have been recalled to the squad for the four-test series alongside two previously uncapped players in left-arm seamer Mark Footitt and explosive opener Alex Hales.
Pace bowlers Mark Wood (left ankle) and Steven Finn (left foot) will miss the tour because of injury.
Former South Africa captain Graeme Smith and ex-wicketkeeper Mark Boucher reacted with glee to news of the England squad.
"Very surprised England have selected Ballance for tour of SA... Thinking our fast bowlers might be licking their lips," Smith tweeted.
Boucher wrote on the social media site: "England without @KP24 (Pietersen) and now @Ian_Bell...I may be wrong, but I'm feeling a sudden boost of confidence throughout SA fans. #interesting."
England arrive in South Africa on Dec. 11 with the first test starting in Durban on Dec. 26. The other three tests are at Cape Town, Johannesburg and Centurion.
England squad: Alastair Cook (captain), Moeen Ali, James Anderson, Jonathan Bairstow, Gary Ballance, Stuart Broad, Jos Buttler, Nick Compton, Mark Footitt, Alex Hales, Chris Jordan, Samit Patel, Joe Root, Ben Stokes, James Taylor, Chris Woakes
(Reporting by Simon Jennings, Rob Hodgetts; Editing by John O'Brien, Neville Dalton)
