After thrashing Czech Republic 4-0 a week ago, Australia laboured to a 2-1 win against the 51st-ranked hosts in Budapest, a performance which left coach Bert van Marwijk underwhelmed ahead of their Group C opener against France.
However, Hull City's Irvine felt it was a match the Socceroos would have let slip in times past.
"I think it's maybe a game we might not have always won in recent times and I think that shows how far we've come," Irvine told reporters.
"We've always had a very good mentality of not losing games but maybe sometimes we've drawn games, particularly in the qualification process, that we (maybe) haven't played particularly well and couldn't quite nick that win.
"It shows the experience that we've gathered as a team and I think as we've grown together, we're finding ways to win games when things aren't going particularly smoothly out there, and tonight was probably the perfect example of that."
The biggest positive for Australia was 19-year-old Daniel Arzani, who scored just 67 seconds after he was introduced as a substitute in the 73rd minute.
He will be the youngest player at the World Cup and although his goal was aided by a goalkeeping error, the highly regarded teenager made an impressive cameo in just his second Socceroos appearance.
"Heading into such a massive tournament it's important to be getting wins going into it and just to get the confidence of the boys up. I think that's what were doing now and doing really well," the Melbourne City man said.
"It's really, really important especially coming up against big teams.
"I'm absolutely buzzing, I can't wait."
Australia take on the French in Kazan next Saturday, before the Socceroos face Denmark in Samara and conclude pool play against Peru in Sochi.
(Reporting by Ian Ransom; Editing by John O'Brien)
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