"It was a better performance, certainly with the ball," said Strauss.
"There was early movement when Graham Onions and James Anderson bowled and Graeme Swann was exceptional, a great spell of spin bowling.
"There was a bit of a wobble which we could have done without, but we just about got over the line."
Man-of-the-Match Swann blamed England's lacklustre performances in the one-day series had been a result of playing the matches after the successful Ashes Tests.
"It has been the classic 'after the Lord Mayor's show', it really has felt like that," Swann said.
"We have been beaten by a very good Australian one-day team. It's good that we managed to grab a win at the end, 7-0 would have been would have been embarrassing, it's bad enough at 6-1 but 7-0 would have been a world record and a horrible world record to hold. We're happy we've avoided that."
But Strauss insisted England will need to dramatically improve their one-day form to have any impact on the world stage.
"We need to be honest and not settle for mediocrity," he added.
"Anyone who has been part of this series does not want to go through this experience again."
Coach Andy Flower agreed that vast improvements had to be made if England are to challenge in South Africa.
"Our batting's been poor, our bowling's lacked wicket-takers which has highlighted how far off a good one-day team we are, so we've got some decision-making to be made," he said.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.