The loss, coupled by wins from Panama and Honduras, meant that the United States have failed to reach the World Cup for the first time since 1986.
"It is the greatest privilege for any coach to manage their country's national team, and as I leave that role today, I am honored and grateful to have had that opportunity twice in my career," Arena said in a statement released by the U.S. Soccer Federation.
"This certainly is a major setback for the senior men's national team program, and questions rightly should be asked about how we can improve.
"No doubt this process already has started and will continue so that U.S. Soccer can progress."
(Reporting by Steve Keating and Frank Pingue in Toronto; Editing by Toby Davis and Christian Radnedge)
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