Goodwin scored Australia's first World Cup goal from open play since Tim Cahill's volley against the Netherlands eight years ago and had the Socceroos in dreamland, threatening another major upset after Saudi Arabia beat Argentina.
Australia were quickly blown away by France, however, and remain without a World Cup win since 2010.
"We've built the belief and the energy and the focus. The last week since we've been in camp, we've been working hard and building that belief. And the way we started, I think that they believed," Arnold told reporters.
"At the end of the day, (it was) the quality of the French team. They are the previous world champions for a reason... But overall, the boys did everything they could and that's all I can ask.
"I thought that we started the game very well...We just got punished by our mistakes. That's that game gone, now it's about winning on Saturday, so we've got to get ready for it."
Australia are bottom of Group D and next face Tunisia, who played out a goalless draw with Denmark.
"It's better that the games are not too far apart as it gives us something to look forward to," midfielder Aaron Mooy said.
"We were trying to be compact through the middle which I think we did okay, but they went around the sides. I think three of the goals were from crosses. Quality deliveries, and the movement, that's why they're world class."
