Galatasaray forward Harry Kewell has been included despite suffering with a groin injury this season.
Verbeek is confident the former Leeds and Liverpool winger will be fit ahead of Australia's first match against Germany in Durban on 13 June.
Williams said: "I'm heartbroken, but obviously proud...just to have got this far.
"I have been struggling for a long time, but the [Socceroos] coaching staff gave me every possible chance to be fit. It obviously just wasn't meant to be."
Although Fifa confirmed it had received the final 23 names before the 1 June midnight deadline, Verbeek only publicly announced his 23-man squad on Wednesday morning.
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Kewell's Galatasaray team-mate Lucas Neill, Everton midfielder Tim Cahill, and Fulham goalkeeper Mark Schwarzer were also included in Verbeek's squad.
But Aston Villa defender Shane Lowry was omitted, along with Netherlands-based midfielders Tommy Oar and James Holland.
Verbeek had reduced his squad to 28 prior to Tuesday's 1 June deadline when he discarded Middlesbrough striker Scott McDonald, Crystal Palace midfielder Nick Carle and defender Jade North.
It means the squad has only three strikers in Josh Kennedy, Harry Kewell and Nikita Rukavytsya.
Brett Holman, who scored the winning goal against New Zealand, can also play as a striker which may be key with Kewell and Kennedy suffering from groin and back injuries.
Australia squad:
Goalkeepers: Mark Schwarzer (Fulham), Adam Federici (Reading), Brad Jones (Middlesbrough)
Defenders: Lucas Neill (Galatasaray), Craig Moore (unattached), Scott Chipperfield (Basel), David Carney (Twente Enschede), Luke Wilkshire (Dynamo Moscow), Mark Milligan (JEF United), Michael Beauchamp (Al-Jazira)
Midfielders: Tim Cahill (Everton), Mark Bresciano (Palermo) Vince Grella (Blackburn), Brett Emerton (Blackburn), Jason Culina (Gold Coast), Brett Holman (AZ Alkmaar), Carl Valeri (Sassuolo), Mile Jedinak (Antalyaspor), Richard Garcia (Hulll), Dario Vidosic (Nuremberg)
Forwards: Josh Kennedy (Nagoya), Nikita Rukavytsya (Twente Enschede), Harry Kewell (Galatasaray)
Source: BBC Sport
Source: BBC Sport