Ian Bell and James Taylor were dismissed for ducks by Mitchell Starc in the first three balls of the match before Morgan struck a century to drag is team to 234.
Starc (4-42) and fellow seamer James Faulkner excelled in the absence of rested paceman Mitchell Johnson, who ran through England in the 2013/14 Ashes to take 37 wickets, before David Warner drove Australia to victory with 127 off 115 balls.
“I suppose the overall feeling is very disappointed,” said Morgan, who replaced Alastair Cook as captain last month. “Losing wickets so early on in our innings really set us back and I thought from there we did really well to get 234.
“If we’d have posted 280-plus, we’d have been in with more of a chance in the game, but being 0-2 to start with was a bit of a shock.
“But Australia are a strong side and they can come up with performances like that, we’ve just got to find a better way of dealing with them.
“We came into the game with a lot of good preparation under our belt and within the side we would have had a lot of expectation on ourselves, so we have a lot of disappointed guys in the changing room.
“Simply, we weren’t good enough to adapt the wicket and play accordingly. We’re going to have to dust ourselves off and come back in four days (against India).???
Meanwhile Starc believes Australia’s victory could revive bad memories of last winter’s Ashes tour.
“Hopefully we reopened a few scars,” said the left-arm paceman. “They’re going to have to be out here for a few months now with this Tri-Series and the World Cup so there’s no better way to kick off our campaign than getting one above them.
“I think we played really well with bat and ball, showed great intensity, and the only way to go is to try and improve on that.
“I guess blokes bowling at 140-145kmph (87-90mph) plus is handy. It has that intimidation factor towards some of the batsmen,” he added.
“It’s also about execution but having that pace is good. Pat bowled a few at 150kmph today and we obviously have Mitch coming back in at some point bowling rapid as well. It’s a great combination.”