"What I've learned more than anything is: don't lose your first game, whatever happens," the Liverpool midfielder told British media.
"It's great to win it and get off to a flying start but if you can't get that win, make sure you are solid and don't concede late on looking for the winner.
"Make sure you get a solid start, at least a draw, because as soon as you lose that first game in a three-game group you put yourselves under pressure straight away. That's the biggest thing."
England drew criticism for the manner in which they played during their drab 1-0 win over Portugal in their final warm-up game on Thursday but Milner said the team would raise their game at the tournament.
"We've had three wins out of three against different, but difficult, opposition without playing our best football," he added of the 2-1 wins over Turkey and Australia prior to the Portugal match.
"We've got gears to go through and we want to peak at the tournament," he added.
"We can play a variety of formations, there are players with so many different strengths -- pace, trickery, solid players and more defensive-minded players -- so I think as a squad we've got so many options."
Wales and Slovakia are England's other Group B opponents.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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