The Britannia Stadium club have abandoned their pursuit of the United States international, after a second work permit application for the 21-year-old forward was denied
The United States international, who has 18 caps for his country, joined on a free transfer from New England Revolution in January, despite being denied a work permit two months previously.
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And Hughes has conceded that the decision effectively ends Stoke's hopes of signing the player.
"We are desperately disappointed for the boy himself because he's made a big effort," he told the Stoke Sentinel.
"He came to us and then went out to Holland because he wanted to do everything in his power to help himself.
"Unfortunately, that's probably the end of it. You never say never, but we would probably have to wait something like two years for him to play the required number of games."
Hughes will take the Agudelo saga into account as he plots his close-season transfer dealings.
"I just think that given what seems to be happening, it's very unlikely Stoke City will be going to any work permit hearings in the near future," he added.
"There would be no point, given the attitude to bringing in non-EU players, if they are not £20m to £25m players because it's very unlikely we would get them in.
"For full internationals with great potential, there is no pathway."