After being thumped 4-1 in its group opener by France, Australia responded with back-to-back 1-0 wins over Tunisia and Denmark, reaching a last-16 tie against Argentina.
Graham Arnold's side threatened an upset on Sunday (AEDT, too, but eventually went down 2-1 after Messi inspired La Albiceleste to victory.
Socceroos coach Arnold said of Messi, who scored the opener: "Look, he's incredible, one of the greatest ever.
"We worked really hard to not be in awe of him, because of the great player he is, but he's remarkable.
"I had the privilege of playing against Diego Maradona and now of coaching against Lionel Messi on a few occasions.
"They're both wonderful players and Argentina should be so proud and happy they've produced players of that calibre."
Kuol, who at 18 became the youngest player to feature in a World Cup knockout match since Pele, could have netted a late leveller, only for Emiliano Martinez to block well.
18 - Aged 18 years and 79 days, Garang Kuol is the youngest player to play in the knockout stages of the World Cup since Pelé in 1958 (17 years, 249 days). Double-take. pic.twitter.com/ZCCPopK0UR— OptaJohan (@OptaJohan) December 3, 2022
"I was telling myself that I'd come on and score a goal and Arnie was telling me to come on and do the same thing," Kuol said.
"We had the same expectation.
"When I wasn't able to score I was very disappointed but we move on.
"I didn't really see much of it. I just turned around and tried to shoot. It was only when I saw the replay I could see the keeper rushed out.
"It's just a learning curve."
Although Australia came up short against both France and Argentina Kuol felt the performances were evident of a narrowing gap between the Socceroos and elite opponents.
"Yeah, 100 per cent," he said.
"People think the people in Europe can fly or something but we're all humans, we've all got two feet.
"It's all just about the passion and the heart."
"I haven't even thought about it," he said. "My contract is up and I just want to go away, have a good holiday, have a break and see what happens.
"I've worked extremely hard throughout this campaign, I did the Olympic team for nothing just to help these players come through.
"I need a break and a rest, then I'm sure I'll have good discussions with the federation."