The Potters chief executive says the club have been left "amazed" that their appeal was rejected and claims the decision was made without an explanation from the panel
The United States international had signed a pre-contract agreement with the Potters in hope of making a move to the Midlands club in January.
However, Stoke manager Mark Hughes and chief executive Tony Scholes were unsuccessful in presenting the Britannia Stadium outfit's case to a panel in London on Wednesday.
And Scholes has been left disgruntled by the decision, which he believes was unjustified.
“We’re bitterly disappointed that the panel rejected our appeal for a work permit for Juan," he told Stoke's official website.
“The criteria by which the panel should make work permit application decisions are well established and have been in place for some years and, despite recent comments to the media and discussion in the media, that criteria has not changed.
“We are therefore left amazed that our application for a work permit for Juan has been rejected when you compare his talent and ability to players who have been granted a work permit on appeal in the past."
The Potters will be unable to appeal the panel's ruling, and Scholes insisted an explanation was not provided as to why Agudelo would not be granted a work permit.
He said: “Unfortunately, under the rules of the appeal panel system we were given no explanation why the application was rejected and so can only speculate as to the reasons why we have been unsuccessful.”