Australia stopper Jones returns home
Jones, a regular understudy to first choice Mark Schwarzer, left on Saturday, less than a week before the start of the June 11-July 11 tournament in South Africa.
"We decided to let him go to his family and let him stay there as long as he likes," Verbeek said at a press briefing at the team's training camp near Johannesburg.
"We expect him not to come back, that says enough about the seriousness of the matter."
Jones could return if he wanted but the team had asked FIFA to name a replacement, Verbeek said.
Goalkeeper Eugene Galekovic has been training in South Africa despite not being part of the official squad and is the most likely replacement.
Australia kick off their Group D campaign against Germany on June 13 and also play Ghana (June 19) and Serbia (June 23).
Socceroos captain Lucas Neill said the whole team had been affected by the news, which had made the warm-up game against the United States, which they lost 3-1, particularly difficult.
"It hit all the boys for six, as we say in Australia, it took us all back," Neill said.
Verbeek also told reporters that Tim Cahill, a key player in the side, would be back in training on Monday after a hospital check-up showed a neck injury suffered in the defeat to the U.S was not serious.