Iran missed out on qualifying from the group stage on goal difference after having a stoppage-time winner against Egypt disallowed for a marginal offside.
Coach Amir Ghalenoei said his team were the "most oppressed" at the tournament amid the backdrop of the country's conflict with the US and Israel.
Iran's training base was switched from Arizona to Tijuana in Mexico before the World Cup began and they faced travel restrictions throughout.
Despite Saturday's 1-1 draw with Egypt, Iran still had a chance of qualifying as one of the eight best third-placed teams.
But their elimination was confirmed when Algeria and Austria played out a dramatic 3-3 draw on Sunday.
Speaking to reporters on Monday, secretary of the Department of Homeland Security Markwayne Mullin said: "I'm just glad they're done, and they're not coming back.
"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 added: "There wasn't a single team that we had to spend more time dealing with than Iran."
Iran were only permitted to enter the US the day before their first two matches and had to leave on the same day as the game, under the terms of their visas.
Those restrictions were eased for their final group game in Seattle, allowing them to arrive two days early, but they again had to return to Tijuana after Saturday's match.
Iran coach Ghalenoei said that the US, co-hosts of the World Cup with Canada and Mexico, had "treated us very unfairly" and that his squad had been given "less than half" the training window it needed to prepare.
Iran captain Mehdi Taremi added: "This kind of tension undermines the joy of the World Cup. I felt the tension from the first moment we arrived."
