Markwayne Mullin, the Secretary for the US Department of Homeland Security, said he was "so happy" that Iran were out.
"I was so happy when we were able to pull their visas and said they could leave the US soil, and I might've sung a song or two or maybe even danced a happy dance," he said at a security briefing.
Iran's football federation responded with a statement in which they said they were unsurprised by the comments, and said it underscored the fact they had never been welcome at the tournament in the first place.
"These remarks once again demonstrate that US officials have no commitment to international law or the principles expected of a host nation capable of organising a global sporting event," the statement read.
"The fact that he openly celebrates Iran's elimination says far more about him than it does about our team. It reflects a level of pettiness that cannot even tolerate the presence of a football team competing on the world's biggest stage."
Iran came close to qualifying for the last 32 after drawing all three group games, and were denied victory against Egypt in their final game by a marginal offside call.
The Iranian federation made multiple complaints over their treatment at the hands of the US authorities during their time at the competition, with their coach Amir Ghalenoei saying his team were the "most oppressed" at the World Cup.
Iran moved their training base to the Mexican border city of Tijuana in May, having originally been due to be based in Tucson, Arizona. All three of their matches were played in the US – with the first two in Los Angeles and the last one in Seattle.
One of Iran's complaints during the World Cup was the stipulation from the authorities that they leave the US immediately after each match.
Asked about that, Mullin said: "That was just an agreement we had – to just go ahead and let them go.
"The game was over, let them get back to the hotel, their base camp where they're at. They're more comfortable there. That was just an agreement we worked out with FIFA before the games started."
Mullin said "almost half" of Iran's non-playing delegation had direct ties to the Islamic Revolutionary Guard Corps (IRGC).
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