Stoke were blocked from signing Agudelo by a UK work permit panel.
Hughes is angry that Stoke are not entitled to an explanation for the panel's decision - and insists their case was a powerful one.
"It was not a frivolous attempt to get a player in," he complained.
"The club invested a lot of time, effort and finance. There's not too many players we have brought in from outside the EU, so we haven't got a reputation for getting any old Tom, Dick or Harry in.
"We had an opportunity to bring in a very exciting talent who most people think is one of the most exciting players in the US at the moment."
He admitted that Agudelo hadn't played the requisite number of internationals in the past two years, despite his 17 caps by the age of 20, but there was a testimonial from US boss Jurgen Klinsmann insisting he would have been selected but for injury.
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