Australia feeling confident after easing nerves with Ireland victory
A second-half penalty from stand-in captain Steph Catley gave the co-hosts a 1-0 win in Group B, with regular skipper Sam Kerr missing out through injury.
It was Australia's first win in a Women's World Cup opener since 2007, when they reached the quarter-finals.
"It's so important. We've talked about this for the last three years in our preparation, that this first game will really dictate how we go in this tournament," Carpenter said.
"It wasn't the prettiest game of football, Ireland are very physical ... Sometimes you just have to win, it doesn't have to be pretty.
"Now that we've checked that first game off, got out of all the nerves, I think we're really going to hit the ground running next game."
Kerr, her country's all-time leading scorer with 63 goals, will also miss their second match against Nigeria in Brisbane next week after sustaining a calf injury in training on Wednesday.
"We know that she was with us throughout the whole 90 minutes and we played for her, we won for her," Carpenter said. "We know that she'll be back with us soon.
"We're all there for her like she's always there for us during (tough) times ... We'll all rally around her and we know that she'll get herself right to come help us in the later stages."
