Head of selectors Omar Henry told the South African Press Association on Saturday that Symcox was finding it increasingly difficult to balance the job with his commitments as a television commentator and newspaper columnist.
"I didn't ask him to leave," Henry was quoted as saying. "I'm disappointed to see him go."
Symcox described the South African bowling attack as the worst in 40 years during the tournament.
The hosts crashed out of the cup after tying a rain-affected match against Sri Lanka.
Captain Shaun Pollock suggested after the game that they had mis-read a Duckworth-Lewis scoring table detailing their revised victory target. His side ended on 229 for six when one more run would have got them into the Super Sixes.
