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 with distinction.
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.
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 goalscorer 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 Lampard, Ashley Young - they all represent a real threat," he said before Lampard, a one-time team mate at Chelsea, was ruled out with an abdominal injury.
Shevchenko is the all-time top scorer for Ukraine with 46 goals and was European Footballer of the Year in 2004. he scored 175 goals for Milan between 1999 and 2006, winning a Champions League final in 2003. A later spell at Chelsea proved disappointing.
Whether he plays or not is likely to depend on a thigh injury and a persistent back problem.
"I have had this twice," he said, slapping his problematic right thigh. "But I still have time to prepare myself."
He has also to impress Blokhin - himself a legend of Ukrainian football in Soviet times and a former European Footballer of the Year too.
Asked in March about Shevchenko, Blokhin replied laconically: "Names do not play football ... If they did, I could be playing now."