The AFC giants were handed a daunting clash with Copa America champions Argentina in the last 16 and fell to a 2-1 defeat despite a valiant effort on Saturday evening.
Lionel Messi and Julian Alvarez put Argentina two goals to the good on the night, and Australia could not claw their way back into the game following Craig Goodwin's deflected response.
Defeat to Argentina at the Ahmad bin Ali Stadium prevented the Socceroos from reaching their first-ever quarter-final, and Arnold's contract as manager has now expired.
When questioned on his future with the national team after the game, Arnold insisted that he wanted to take a break before holding "good discussions" with Football Australia.
"I haven't thought about the future. My contract is up and I just want to go away, have a holiday, have a break and see what happens. I've worked extremely hard in this campaign," The Guardian quotes Arnold as saying.
"I haven't even thought about it. I need a break, a rest and no doubt I'll have some good discussions with the organisation."
Australia succumbed to a sublime Messi finish with 35 minutes gone in their last-16 clash, and Alvarez doubled La Albiceleste's lead after robbing goalkeeper Mathew Ryan of the ball.
However, with 13 minutes remaining, Goodwin's long-range effort took a significant deflection off Enzo Fernandez into the net to give Australia a glimmer of hope, and a mazy run from Aziz Behich ended with the left-back's shot from close range being blocked by Lisandro Martinez.
Newcastle United-bound teenager Garang Kuol then had an effort saved by Emiliano Martinez right at the death, and while he expressed pride in his players' performance, Arnold admitted that a last-16 place was "not enough" for him personally.
"I just wanted to win so badly for the nation, the fans and the game of football in Australia. Making the last 16 wasn't enough - I wanted more," the 59-year-old added. "That's just me. I know some people may be happy with it, but that's just the way I am. I felt we failed tonight.
"I just said to the boys I couldn't be more proud of the effort and everything they gave to me, and to the nation. It's been a four-and-a-half-year journey, a tough journey for everyone.
"We're a bit disappointed as we could've got something more out of it, but I hope Australia is proud of these players. Everyone said before we came here we were the worst Socceroo team ever to qualify for a World Cup, but that's gone now.
"We've done exceptionally well, making the last 16 and winning two games. The mixture of the young boys and senior boys has worked well."
Arnold also publicly called for more government funding into Australian football following their second World Cup last-16 elimination, having first reached the knockout stages in 2006.
"We need to spend money and get help from the government to put some money into the game and develop kids," Arnold added.
"One thing I'd love to see before I finish up completely from football is that the government build us a house - we've been homeless since I've been involved for 37 years - a facility that can inspire, something like the AIS, something the government can fund for the national teams and for the good of Australian football."
Argentina will now take on the Netherlands in Friday's quarter-final after Louis van Gaal's side overcame the USA 3-1 earlier on Saturday.