Sleightholme, 24, came on as a replacement and scored twice in the second half to register his first two international tries.
Marcus Smith’s touchline conversion from the Northampton wing’s second try put England into a 30-28 lead heading into the final 10 minutes.
However, two Wallaby tries – either side of Itoje’s 78th-minute score – saw Australia register only their second win against England in their past 12 meetings.
The frantic finale also prevented a dream first game at Allianz Stadium for Sleightholme, who won his third cap on Saturday.
“It was nice to score but it doesn’t mean anything if you don’t win,” he added.
It is the fourth game in five matches that Borthwick’s side have fallen on the wrong side of the final play, following two close Tests against the All Blacks in July and a 33-31 defeat by France in their final game of this year’s Six Nations.
On Saturday, England will face world champions South Africa, who defeated Scotland in their opening match of the autumn on Sunday.
“We’re testing fans’ patience, testing our patience,” admitted England number eight Ben Earl. “It feels like we won the game twice against Australia and then managed to lose it. Frustrating.
“Not the same old problems, different problems, but the same overwhelming feeling of another game that we’ve let slip. So food for thought.”