Obviously delighted with the win, Jones says the Wallabies are the ones under the spotlight going into next weekend's second Test in Melbourne.
"There's a lot of expectation about the Wallaby team," Jones said.
"They've come back as the second-placed team in the world. "They've got the world's best coach and the expectation's high for them. The pressure's on them next week."
England will travel south in buoyant mood but Jones says if his team is to secure a series win they'll need to improve.
Australia raced to a 10-0 lead after a fast start and came home with a wet sail after being outmuscled by the tourists in the middle section of the Test.
With the Wallabies scoring four tries to three, Jones is aware Saturday's result could've been a different one.
"We're obviously happy with the result but we didn't play well," Jones said.
"We gave the Wallabies some easy tries and need to do some work on our defence.
"We made history today but it's not good enough for us. It's all about next week."
Australia 28 (M. Hooper 2, I Folau, T Kuridrani tries; B Foley con, 2 pens) England 39 (J. Joseph, J. Nowell, M. Yarde tries; Owen Farrell 3 cons, 6 pens). Halftime: 13-19.
- AAP, AP