The 20-year-old signed a pre-contract agreement with the Potters in August and had been expected to move to the Britannia Stadium in January when his deal with Major League Soccer side New England Revolution expired.
Stoke chief executive Tony Scholes and manager Mark Hughes presented the case at a hearing in London on Wednesday but the panel rejected it and the Potters have no right to appeal the decision.
Scholes said on stokecityfc.com: "We're bitterly disappointed that the panel rejected our appeal for a work permit for Juan.
"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.
"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."
Colombian-born Agudelo represented the US at Under-17 and Under-20 level before making his full debut against South Africa in November 2010, where he scored the only goal of the game.
He has won 17 caps for the States but was not included in Jurgen Klinsmann's squad for the past week's friendlies against Scotland and Austria.
Source: PA
Source: PA