The Australians, who won the title on home soil four years ago, dominated for long spells but were unable to find a way to cancel out Anas Bani Yaseen's 26th minute header in the Group B clash at Hazza bin Zayed Stadium.
"It was one of those days," Arnold said.
"A frustrating day and the ball didn't seem to bounce. But you've got to give full credit to Jordan and they've shown that they had a lot of fight."
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Australian players walk on the pitch after losing the 2019 AFC Asian Cup football game between Australia and Jordan at the Hazza Bin Zayed stadium in Al-Ain on January 6, 2019.

Image credit: Getty Images

Vital Borkelmans' Jordan were resolute in defence against an Australia side that struggled to turn their domination into chances. The Socceroos went into halftime trailing by a goal and were fortunate not to be further behind.
Bani Yaseen put his side in front when he was given the time and space to head Baha Abdelrahman's corner home unchallenged, powering the ball beyond the flat-footed Maty Ryan.
Four minutes later Abdelrahman almost added a second when his freekick from the edge of the area speared towards goal, only for Ryan to push the ball onto the woodwork before it was cleared.

Jordan's players celebrate after scoring a goal during the 2019 AFC Asian Cup football game between Australia and Jordan at the Hazza Bin Zayed stadium in Al-Ain on January 6, 2019.

Image credit: Getty Images

For all their possession, Australia crafted few clear-cut opportunities, with Awer Mabil's shot coming back of goalkeeper Amer Shafi's legs and Jamie MacLaren heading high over the bar.
Mabil hit the woodwork late in the second half as Australia grew increasingly desperate to find an equaliser and Shafi was kept busy until the final kick of the game. However, Jordan held on for a famous win.
Australia next face Palestine on Jan. 11 while Jordan will take on Syria.
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