Ange Postecoglou's side ended their 2014 FIFA World Cup campaign without a point after the world champions eased to a 3-0 triumph in Curitiba.
It was a disappointing way for Australia to bow out of the tournament, given their impressive performances against Chile and the Netherlands, despite both games ending in defeat.
Australia's bold and daring approach won many admirers in Brazil, but Jedinak felt the intense nature of their first two matches cost them against Spain.
"They (physical and mental exhaustion) definitely both come into play with the way the games have gone. They've been such high intensity all the way through," Jedinak is quoted as saying in The Age.
"But at this level, it (is) something you have to deal with if you want to play against this sort of opposition. That's the level we've got to try and get to.
"It was tough (against Spain). We started really well but we let them back in and obviously we know the quality they've got.
"It's been a disappointing tournament by their standards but we knew that wouldn't mean anything and they'd want to make it right.
"We were a little bit unfortunate…we conceded three goals and that's what you get against quality opposition."
Jedinak still looked back on the campaign fondly, though, as the midfielder – appointed skipper earlier this year – relished the responsibility on the big stage.
And he has now targeted success in the Asian Cup, which Australia will host in January, as his side's next goal.
"I've been honoured to lead this bunch of boys in the heat of battle at the World Cup on the biggest stage," he added.
"Obviously I've had some great support from my team-mates and the senior players in the group.
"Not only that but we just bonded together and you can see out there we don't want to let each other down.
"We were working doubly hard for each other. That showed, and I can't fault anybody.
"The team has grown, we know that, and we know some of the stuff we play (is competitive).
"It's about now taking the next step and turning those positives into results and points. We've been challenged to get better, not only individually but collectively and that starts now."
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