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The hosts, who beat India in a thrilling final at Lord's, will travel down under in October as they try to regain the Ashes they lost in 2015.
"We have to stay really humble as a team. There's a lot more growth in them and we're not perfect," said Robinson.
Clare Connor, the ECB's director of women's cricket, is determined to ensure the victory is not a "one-off".
Sunday's match, played in front of a sell-out crowd, is thought to have attracted the largest television audience for a women's cricket match - of up to 100 million people.
"The Ashes will be a big test, but we'll go there with momentum and confidence. What would really cap a special year is bringing the Ashes home," said Robinson.
He added the women's game must "capture the moment" but is cautious about talk of further global T20 leagues being established alongside existing competitions in England and Australia.
"It concerns me a little because we want as much contact with the players as we can," said the former Sussex coach.
"We don't play enough international games, so the thought of losing the players to more tournaments doesn't sit right at the moment."
This World Cup represented a huge shift in the exposure given to the women's game.
Four years ago in India, matches were well-watched on TV, but poor attendances at grounds hinted at a lack of a lasting legacy in the host nation.
Now England has staged a successful competition, Connor said it must be built upon.
"We can't miss this opportunity," she told BBC sports editor Dan Roan.
"We've got a wonderful team of amazingly talented, humble young women who have lifted a trophy on home soil in front of 27,000 people in a stadium and goodness knows how many on the screen.
"That gives us an amazing opportunity to cash in that success to secure greater investment, to continue to drive the business case and commercial viability of the sport and continue to invest in the pathway and the talent pool so this can't be a one-off."
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England captain Heather Knight said she hoped the success of the World Cup would lead to an increase in international matches.
Before the tournament began in June, England had not played a full one-day international since November.
"Talk of a women's Indian Premier League is exciting, but, first and foremost, we need more internationals," she said.
"Outside of tournaments, we haven't played the likes of Australia and New Zealand for a long time and it is the games against the best opposition that make you better.
"Coming into this competition, we didn't know how we'd go against the bigger sides because we hadn't played them. Luckily it went well, but we'd love to do it more often."
The World Cup represented a personal triumph for Sarah Taylor, who returned after more than a year away from international cricket because of an anxiety-related problem.
The 28-year-old wicketkeeper will "take time" to reflect, but expects to remain available for England.
"Health-wise I'm in a good place," she said. "I want to be part of this team because these girls are family to me.
"I'm not going anywhere soon."
England coach Mark Robinson is targeting the Ashes after his side won the Women's World Cup on Sunday.