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The Roses recovered from going seven goals behind to lead the world number one side in the third quarter.
With 10 seconds to go, England needed only one goal to take the game to extra time, but Diamonds captain Sharni Layton produced a match-winning interception at the death.
Australia finish the series with three wins from three matches.
England won their opener against South Africa in extra time, before being comprehensively beaten by New Zealand in Liverpool.
But coach Tracey Neville was pleased with the turnaround in their performance against the world and Commonwealth champions.
"I'm so proud of them. I said to them they had to back each other on court," Neville told BBC Two.
"There were some of the critical moments where we could have got ahead but we have to look at positives.
"They fought from the start to the end. We made them make changes and you have to challenge the coaches as well as the players."
England defender Geva Mentor, who was named player of the match, added: "We turned it around from the lousy performance in the week.
"The Wembley crowd got us over the line. I'm so proud of the team."
In the final game of the series New Zealand beat South Africa 70-39 to leave the Proteas winless with three defeats.
Australia retained the Quad series title after a dramatic 47-46 win over a much-improved England at Wembley.