Williams has been named in Australia's preliminary 31- man squad for this summer's finals but he is by no means certain to be included when the final party has to be announced on June 1.
Verbeek and his medical staff have been in contact with their counterparts at Boro to weigh up how his long-standing pelvic problem should be treated.
But the Australia boss has been stunned to learn Strachan had been playing Williams at the end of the season, despite knowing the injury could prevent him from playing in the finals.
The 21-year-old played in the draw against Coventry the week after fading hopes of a Championship play-off place came to an end at West Brom when Verbeek thinks he should have been resting.
Rhys did enough for Middlesbrough.
He played for five, six weeks with an injury and he had an injection every week, said the Dutchman.
I think Strachan should have known how good it is for a player to go to the World Cup. He showed no respect at all towards Rhys and I think that's bad management. I could not understand that.
Strachan had an unbelievable career as a player, so he should understand how important it is for a player to go to the World Cup. He made it very difficult for him.
Williams has been working with physios in Melbourne since his appearance against Coventry, when Strachan's options were limited because of a crippling injury list.
The midfielder, who played three times for his country as a right-back after switching allegiances from Wales last summer, remains hopeful of playing in South Africa and he is due to meet up with the squad for a training camp next week.
Verbeek did not expect Strachan, who played for Scotland in the 1982 and 1986 finals, to show too much consideration for Australia, just towards one of his players.
I was a club manager myself so I know how difficult it is, he said. He's not focusing on Australia, he doesn't care about Australia.
Strachan let him play with injection and it's the worst thing you can do as a manager let a player of his age play with an injection.
Verbeek spoke out after realising the extent of Williams' problem, knowing it is just weeks since Strachan admitted his player had a problem.
Speaking before Williams' return to Australia, Strachan said: Rhys hasn't really been training during the week. I've told him I've been through that before, I had a hernia problem and had to go through until the end of the season and deal with it.
As well as Williams and compatriots Brad Jones and Scott McDonald, plus New Zealander Chris Killen, there are likely to be a couple more absentees when Strachan takes his squad to La Manga this week for a training camp.
Dutch winger Marvin Emnes has been in Germany for a trial with Fortuna Dusseldorf ahead of another season in the second tier of the Bundesliga.
Emnes, who cost £3m during Gareth Southgate's time in charge, has two years left on his contract at Middlesbrough.
Any transfer like this would only be possible on loan terms, said Fortuna boss Norbert Meier, who has been impressed during Emnes' appearances against part-time opposition.
Strachan also hopes to have offloaded Frenchman Didier Digard by the time pre-season begins in late June, but Nice have turned down the chance to sign him full-time.
Digard has impressed during his loan to France but Nice have told Middlesbrough that they cannot afford their £4m valuation, nor his Premier League wages.
Source: Northern Echo
Source: Northern Echo