Coach Amir Ghalenoei didn't say who ordered the Iranians to leave earlier than planned.
The team had been expected to spend the night in California to maximise the normal recovery process after their opening game, only to be told after the match everyone had to immediately get on a plane for the trip back to Tijuana.
"They didn't even give us time to recover," Ghalenoei said through an interpreter. "After the game today, they said to us, 'You have to leave immediately.'
"It's very important for us to have time for recovery, (but) we are asked to get on a plane and return to our camp in Tijuana, and we are really troubled by that."
The Iranians' World Cup cycle has been in upheaval since the US and Israel began a war against Iran on February 28. Iran ultimately decided to compete even after FIFA rejected a request to move their three group-stage matches out of the US.
"We don't know why they are returning us, to be honest," Ghalenoei said. "I think it's very strange. It seems like others are doing the planning for us.
"The decision-making for us is being made elsewhere. We were supposed to come two nights before the game, and we were supposed to stay tonight to recover and return tomorrow at lunchtime. We have no idea why.
"I think our team is perhaps the most oppressed in the World Cup."
Captain Mehdi Taremi and Ghalenoei both decried the team's lack of many important staff members, including the president of Iran's football federation, coaching support personnel and media officials, who were all denied visas by the US, amplifying the team's difficult preparations.
"We have to leave Los Angeles right now, and it's not good for us," Taremi said about an hour after the match. "I think FIFA have to help us more than this. ... Everything is like a disaster, actually, for us."
Iran opened their World Cup campaign with a 2-2 draw, overcoming two deficits and getting the equalising goal from Mohammad Mohebbi in the 64th minute in front of a solidly pro-Iranian crowd despite the presence of many Iranian American fans engaged in protest against Iran's government.
Iran's next match is also at SoFi Stadium against Belgium on Sunday.
Earlier, the teams shared the points in a thrilling 2-2 draw with Elijah Just giving New Zealand an early lead in the seventh minute after being served by captain Chris Wood.
Taremi hit the post in the 23rd but his team was level in the 32nd after Ramin Rezaeian collected a loose ball and hit it into the net.
Iran thought they had taken the lead before the break but Ali Nemati's goal was ruled out for offside.
It was New Zealand, however, who were first on target in the second half with Just linking up once more with Wood to complete his brace.
But the Iranians didn't waste too much time and equalised again thanks to Mohammad Mohebbi in the 64th.
Both sides kept the pressure up and it was an open game until the last minute, but the teams eventually had to settle for a point each.
New Zealand are competing only in their third World Cup, first one since 2010, and are still seeking a first win in the tournament.
Iran were one of the first teams to qualify for the event in the United States, Mexico and Canada but at one stage it was even unclear whether Iran would be permitted to play their three group-stage matches in the US.
The national team then moved their base from Arizona to Mexico to avoid further problems.
Agencies
