The former AC Milan and Chelsea striker, a huge name in Ukrainian football for more than a decade, will quit the national side after the tournament, just three months before he turns 36.
Though he has been fighting for fitness, to claim a regular place in the Dynamo Kiev team, he feels he can represent Ukraine one last time at Europe's football feast.
With or without him, Ukraine cannot be written off, he says, even though they are drawn against heavyweights England and France, as well as Sweden, in Group D.
"We have a young team with potential. A lot will depend on how the young players will deal with the psychological factor," Shevchenko told Reuters in an interview at Dynamo's Koncha Zaspa training ground.
"There will be special pressure on them. If they can handle this, we have a good chance of getting through the group.
"The strongest part of our game is a quick switch from defence to attack. We have got a lot of fast players.
"So our game will be built on swift counter-attacks, using the wings... these are the strong cards we have to play. We will try to use them."
National coach Oleg Blokhin, parachuted in to the hot seat only a year ago, is faced with finding the backbone to stiffen a weak and unstable defence, a problem Shevchenko recognised.
"We sometimes have problems in the air and though we have some strong defenders we often make mistakes from set pieces. We have to work on this and correct things, especially with strong teams like England and Sweden," Shevchenko said.
A goalkeeper crisis has also emerged. Andriy Dykan, who plays for Spartak Moscow, is in danger of missing the Euros after suffering head and facial injuries in a Russian Premier League match.
Following a two-year suspension, handed to Olexandr Rybka, for use of a banned diuretic, this leaves Olexandr Shovkovskiy as Ukraine's only fit and experienced keeper.
Ukraine play Sweden in their June 11 opening match and Shevchenko recognised the threat that their formidable striker, Zlatan Ibrahimovic, will pose for the host team's uncertain defence.
"Zlatan is a player of the highest class. He is having a dazzling season with Milan. He is very fit. A lot will depend on how we play as a team against Sweden. We have got to put the accent on team-work," Shevchenko said.
But he said the tall, agile attacker, who is the top goal-scorer in the Italian championship, often disappointed at national level, compared to his club performance.
"The trainers and defenders will be analysing Ibrahimovic's game in detail," he said.
He said French coach Laurent Blanc had improved France since taking over with Karim Benzema emerging as a menace to defences, but said team-work was the quality that would really matter.
"Only team-work will bring success. The England team have a good chance of making the final. Wayne Rooney, Steven Gerrard and Frank
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