Conte was confirmed as Jose Mourinho's long-term replacement in April and will be tasked with rebuilding a Chelsea side that went from champions in 2014-15 to 10th last season.
Speaking in a press conference during Italy's preparations for the tournament, Conte reiterated his loyalty to his current job, in what will be his final challenge with the Azzurri.
"Those who know me well are very well aware that I handle one thing at a time, I try to face them in the best possible way," Conte said.
"The Euro is the end of a two-year journey."
The 46-year-old – who will take up his post with Chelsea after the competition – also added that Italy will need his and his colleagues' full application if they are to make their trip to France a productive one.
"I want to face this tournament in the best way possible, while knowing the difficulties that we didn't expect to have.
"I always talk about work - we need to work with our head down and give all we have to do something beautiful."