Williams was missing along with James Holland, Tommy Oar and Shane Lowry when Verbeek revealed his final squad on Wednesday. Eugene Galekovic, who had been training with the squad as a back-up goalkeeper, was also absent from the list.
The coach blamed English club Middlesbrough for the absence of Williams, saying the 20-year-old could have made it with different handling of his injury, but the player himself refused to join in with that criticism.
"I think (Middlesbrough manager) Gordon Strachan let him play for weeks with an injury...and I think if you do that to a 20-year-old player you take a risk," Verbeek said at a news conference at their Johannesburg training ground.
Williams took responsibility for playing through the injury himself.
"Everyone enjoys playing football and obviously I did not want to miss a game," he said.
Williams, a former Welsh youth international, was born in Perth and switched to Australia after being swayed by Verbeek to play for the Socceroos last year.
Australia play their first match of the tournament against Germany on June 13 and also face Ghana and Serbia in Group D.
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