Celtic had the better opportunities against their English Premier League opponents during the 90 minutes before misses from Giorgios Giakoumakis and Reo Hatate from the spot allowed Anthony Gordon to seal a 4-2 victory for the Toffees in the shoot-out.
Jota came closest to breaching an Everton side content to sit back and hit on the break, crashing a free-kick against the crossbar in the first-half, while Asmir Begovic made a huge save to deny Kyogo Furuhashi after the break before Liel Abada fluffed his lines from inside the six-yard box.
Celtic boss Postecoglou was happier with his side than he was after the surprise 2-1 defeat to Sydney FC in the tournament opener three days earlier.
"It was a lot more like us,” he told Celtic TV. “I thought we played well and dominated the game. Obviously the game lacked goals which is disappointing, you want to give some entertainment to the crowd, but overall I was pretty happy with the way the boys went about things.
“The lads have adjusted a bit more now. I could see in trainng yesterday they were looking more like themselves. I thought we dominated the game and had better opportunities, we just lacked a goal. But overall a much better effort.”
The trip to Australia was billed as a homecoming for Postecoglou – who grew up in the country and went on play for and manage the national team – and he was pleased that a mostly Celtic crowd of over 40,000 inside the Accor Stadium highlighted the scale of the club’s support Down Under.
“It's brilliant to see. That's been the highlight for us,” he said. “It didn't surprise me but even for the lads and everyone associated with the club to see how much passion our supporters have for their football club on this side of the world. The distance doesn't diminish the passion at all. It was great to see them all week. Not just in the stadium but when you walk around town, there's Celtic shirts everywhere. They've made their presence felt and it's been brilliant.
“The personal stuff is not really what resonates with me. I realise I'm part of a special football club. I knew what to expect but it was great to share it with everyone and for everyone to see what I already know. I think it's been a great week for our club. We're a massive football club, a global brand, and the more we grow in these regions and give back, I think we'll get it back in spadeloads.”
Postecoglou revealed Celtic players will now be given eight days off before reconvening for a training camp in Portugal ahead of the restarting their Scottish Premiership title defence with a trip to Pittodrie on December 17.
"The players are well aware of why we're giving them a break,” he added. “It's not because we want them to have a rest it's just to have a mental and physical break from the schedule we've had. But I know at the back of their minds they'll just be waiting to come back.”