The Red Devils saw title challengers Manchester City and Chelsea get off to winning starts on Sunday and the veteran Welshman knows that last season's league runners up will have to be on their game to match their rivals.
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"Being away in your first game is always tough so we’ll have to be up for it," he told the club's official website.
"We've had a decent record there over the years - they’re always good games which can be pretty quick and quite feisty which adds to the atmosphere.
"David Moyes’ teams always work hard and you know you’re in for a battle and that you’ll have to work harder than them to win."
After being pipped to the title on the final day of the season last term, Giggs is hoping United can use the clash with the Toffees to set their stall out for the coming campaign, as they look to regain their domestic crown.
He added: "We can talk about the quality players we’ve got in our squad but ultimately you need to work hard and make sure you start the season off well.
"It’s certainly a good test to begin with and everyone is looking forward to it.
"The manager likes to lay down his ambitions for the season and look in the players’ eyes to see if they’re ready for the challenge and we are. It was a long summer and we can’t wait to get going and put things right this time."