Coach Ange Postecoglou has predicted Celtic FC will take exhibition matches to other overseas countries before returning to Australia again, despite his status as one of the country's most beloved football figures.

Celtic's Sydney Super Cup campaign began with a 2-1 loss to Sydney FC on Thursday and finished in a 4-2 penalty shoot-out defeat to Everton three days later.

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A combined total of 60,000 fans attended the two matches and Celtic supporters made up the majority on both occasions. The 41,121 that turned out to Accor Stadium on Sunday outnumbered any A-League crowd since before the COVID-19 pandemic.

Postecoglou said he was not one for sentimentality but that it had been special to witness the Australian fans' reaction to Celtic's first visit since 2011.

"It's been good to be back home," he told reporters.

"You walk the streets of Sydney and there are Celtic shirts everywhere. It's brilliant to see.

"We know the enormity of the football club but the distance (from Scotland) doesn't diminish the passion of the supporters."

While European clubs will visit Australia for the Sydney Super Cup in 2025 and 2027, Celtic look set to prioritise other international friendlies rather than return to Australia in the short term.

"We've got to share the love around and go to other areas first," Postecoglou said.

"The club realises that its reach is global. Every part of the globe, we've got supporters."

Everton manager Frank Lampard praised the Australian fans of his side, who sit just above the Premier League's relegation zone after 15 games.

"We appreciate it very much that we're supported on the other side of the world, that people watch us in the middle of the night," he said.

"It's a small world these days so it's nice that we can travel here and be here. (The fans) came in numbers."