The hosts have won six of their last nine home one-day series and crushed the Australians 4-0 last year but they lost the last two post-Ashes series, in 2009 and 2010-11.
England comfortably beat Ireland in a warm-up match on Tuesday with Morgan scoring an unbeaten century against the country of his birth.
"We've talked about it in previous series before and this series is no different, we need to turn up, produce our skills, at crucial times we need to stand up and be counted," he told reporters on Thursday.
"I think everybody is aware of the responsibility that's on their shoulders and what is expected."
England rested Alastair Cook, James Anderson, Ian Bell, Stuart Broad and Graeme Swann following the 3-0 Ashes win, but batsman Kevin Pietersen has been selected despite recent knee problems.
Morgan said the hard-hitting right-hander could open the innings, adding that his presence was crucial in a dressing room full of inexperienced players at international level.
"Kev offers a hell of a lot as a senior player and as a batsman," Morgan said.
"As a senior player he leads by example and with the confidence he goes about his business, people rub off on that and that's crucial," he added.
"When I first came into the team he was one of the most senior players and he was a guy you could turn too and ask questions and have no hesitation turning too for a positive option. In that regard he is fantastic to have in the squad."
Australia have dropped batsman David Warner for the series and fast bowler Mitchell Starc has been ruled out with a sore back.
However, despite back problems of his own, captain Michael Clarke said he gave no thought to resting himself ahead of the next Ashes series starting in November.
"It was a no-brainer for me if I wanted to stay here and play the one-dayers," Clarke said.
"I want to play every game I can for Australia.
"I'll prepare today, as I have done over the past few days, like I would if it was the first Test of the Ashes. It's just as important to me.
"I think it's important I'm here with the team and performing and leading from the front."