The result dealt a severe blow to England's hopes of being top seeds for the 2015 Rugby World Cup when the draw is made in London on December 3.
Ashton is thankful the tournament on home soil is still three years away because England need that time to sharpen their cutting edge.
England hung in as Australia dominated the first hour and Stuart Lancaster's men then bossed the final quarter - but they could not convert any of that pressure into points.
On four occasions, the first being with 22 minutes left in the match, captain Chris Robshaw opted not kick penalties at goal in search of a try that did not come.
"I think we cost ourselves the game. We had enough possession in their 22 and we just didn't take our chances," Ashton said.
"I think the right decisions were made from those penalties (to go for touch or quick taps). I thought we had them but we just couldn't find that finishing pass.
"Toby Flood tried to find me through the back and if the pass had gone to hand I would have been through a hole. And then Thomas Waldrom dropped the ball over the line.
"You have to take your chances. Our attack was better (than it was in last weekend's 54-12 win over Fiji) but we are lacking that clinical edge.
"We put ourselves in a position to win that game and that was the frustrating thing."
Ashton's frustration on the field was evident - particularly when Manu Tuilagi ignored him on the overlap and ran straight into two defenders.
Tuilagi had done something similar to Charlie Sharples at the end of the first half but got away with it when he had just managed to score in the corner.
England and Leicester are working hard to develop Tuilagi's skill-set and distribution, but on yesterday's evidence the midfield strongman remains worryingly one-dimensional.
"Manu is a strong lad and he always gets over the gainline so his first instinct is to do that," Ashton said.
"Hopefully the more I can play outside him the more he will get used to it, then he will recognise the difference between running and passing.
"I thought there was a lot of space out there but it is just us getting to that space and finding the right hole.
"That is the frustrating thing - when you can see it unfolding in front of you and it just breaks down. A bad pass or we end up giving the penalty away."
Tuilagi's try came minutes after Nick Cummins had scored his first for Australia and it gave England a 14-11 half-time lead against the run of play.
Australia were the smarter attacking side with the variety offered by Kurtley Beale and Berrick Barnes a lesson to England about how to use twin playmakers at fly-half and full-back.
The Wallabies edged the scrum battle until Joe Marler was replaced by Mako Vunipola and, in openside flanker Michael Hooper - whose father was born in Kent - they had the man of the match.
There was some debate about whether Tuilagi had actually managed to ground the ball on the whitewash as he stretched for the line but the try was given by television official Jim Yuille, who had a busy day.
Yuille was asked to adjudicate on potential tries from Wallaby prop Ben Alexander, where the pictures were inconclusive, and later from Waldrom, where they were not. Both were ruled no try.
Australia turned the screw after the interval with Barnes kicking three penalties in quick succession and it was only when England introduced Joe Launchbury, Tom Wood and Vunipola from the bench that Lancaster's men built any consistent pressure.
"The intention is to bring as much energy as possible off the bench but it wasn't enough. We felt like they were going to crack any minute but we couldn't finish them off," Wood said.
"It does feel like a missed opportunity."
England only have six days until South Africa arrive at Twickenham. The weekend after that it is world champions New Zealand.
Wood insists England must draw inspiration from the Wallabies, who responded to a 33-6 defeat in France to regain the Cook Cup at Twickenham.
"Australia have set a precedent that when things go wrong and you are written off, that is they way to bounce back and that is what we must try and do," Wood said.
"The right things were said after the game about being harder on ourselves and not letting chances like that slip. It is about when you get a chance at international level - nail it.
"It will be a huge physical challenge next week. We have to get our head around that and face them head on, go after them and bring the fight to them."
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