Drinkwater, who made his England debut in March, faces stiff competition for a midfield berth from experienced internationals like Jack Wilshere and Jordan Henderson, who have both recently returned from injury.
"The midfield has a lot of quality and the players we are talking about have ridiculous quality. They have played at the top level so I would understand (if I did not go to the Euros)," Drinkwater told British media.
"I'm just trying to do what I'm best at and if that doesn't get me in then I'll have to hold my hands up."
England have warm-up matches against Turkey, Australia and Portugal before they face Russia, Slovakia and Wales in the 24-team tournament in France.
(Reporting by Nivedita Shankar in Bengaluru; editing by Sudipto Ganguly)
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