The US started the night in the third qualifying place but ended up fifth after losing 2-1.
Panama jumped up to third after an 88th-minute winner against Costa Rica to reach their first World Cup finals.
However, it was their opening goal that caused debate with Gabriel Torres’ header not appearing to cross the line.
The 52nd-minute equaliser came from a corner with Torres’ effort hitting the post and as Blas Perez tried to force the ball over the line, Ticos defender Ronald Matarrita looked to have cleared it.
However, despite complaints from the visitors, referee Walter Lopez of Guatemala gave the goal.
Honduras beat already-qualified group winners Mexico to also leapfrog the US and secure fourth spot in the table and a two-leg play-off against Australia.
The US beat Panama 4-0 just last Friday but, despite playing a Trinidad & Tobago side with just three points from nine games before kick-off, never looked close to securing a place in Russia.
“We had everything there for us,” coach Bruce Arena said.
“We failed on the day. No excuses. We failed today. We should have walked off this field with at least a point. We should not be staying at home for this World Cup and I take responsibility.”
Omar Gonzalez stretched to cut out a cross and only succeeded in steering the ball past veteran goalkeeper Tim Howard, before Alvin Jones rocketed in a superb 35-yard strike to double the hosts’ lead.
Borussia Dortmund teenager – and star of the win in Panama – Christian Pulisic gave the US hope soon after the restart with a fine long-range goal of his own, but with Honduras beating Mexico it looked like a play-off place for the States.
And then, with time running out in Panama City, Torres – who plays his club football in Seattle – latched on to a long ball forwards and smashed in off the crossbar to send Panama through and leave the US in the wilderness.
‘The most surreal and embarrassing night in US soccer history’
In contrast to Panama, the United States has a population of 323.1 million. Their opponents on Tuesday, Trinidad and Tobago, have a population of 1.3m – roughly the same as the US state of Maine.
Described as the “most surreal and embarrassing night in US soccer history” and “simply devastating” by American journalists, the players were left in tears following their shock 2-1 loss.
“It’s a blemish for us. We should not be staying at home for this World Cup and I take responsibility,” coach Bruce Arena said.
“We failed on the day. No excuses. We failed. We should have walked off this field with at least a point.”
Captain Michael Bradley described the night as the “perfect storm.”
“Everything that could have possibly gone wrong did, in this stadium and in two other stadiums across the region,” he added.
“To give away the first goal like that [on an own goal] is a killer. But the reality is it was all there for us, and we have nobody to blame but ourselves.”