Coach John Bracewell said Monday the 35-year-old Cairns was not chosen due to "issues with his cricket fitness" but the door remained open for his return.
Cairns said he was upset at being left out of the side to play one of his favourite opponents but said he was determined to fight his way back.
"The pride's been dented, of course, but I've had time to come to terms with it. There's two ways; I can either fight it or say goodbye, and I'm not done yet," Cairns told the New Zealand Press Association.
His game has suffered through a lack of match play since retiring from Test cricket last year and he has not played any first class matches since the middle of 2004. But he will return to local first class cricket over the coming season in an attempt to turn his fortunes around.
"I want to make sure that I end when the terms are right and when I'm happy. I'd still like to keep going."
Bracewell has thrown down the challenge to the injury-prone star to play his way back into the team.
"He is focused on playing in the World Cup and will have plenty of opportunity to return to form and full match fitness over the domestic season," Bracewell said in a statement.
"He will be considered for a return to international cricket later in the summer," Bracewell said.
Cairns, considered one of the world's best all-rounders in his prime, has been replaced by left-arm swing bowler James Franklin in the only change from the recent tri-series one dayers in Zimbabwe.
Cairns failed to impress in the early matches of the tour and was ruled out of the later games with persistent hamstring problems.
He retired from Test cricket after becoming only the sixth player in world cricket to score 3,000 runs and take 200 wickets. He was the Wisden Cricketer of the Year in 2000.
Spinner Jeetan Patel was retained in the New Zealand side after making a solid debut in Zimbabwe, Bracewell said. "He is a long term investment and deserves to be retained for a second tour."
New Zealand will play five one day matches in South Africa starting on October 23, as well as a Twenty/20 game to open the tour.
Stephen Fleming (captain), Nathan Astle, Hamish Marshall, James Marshall, Craig McMillan, Lou Vincent, Scott Styris, Jacob Oram, Brendon McCullum, Daniel Vettori, James Franklin, Kyle Mills, Andre Adams, Shane Bond, Jeetan Patel.