The Ukraine striker insists that if the team play to their potential, it will give them a fighting chance of reaching the final, which will be held at the Olympic Stadium in Kiev
While the former Chelsea and AC Milan ace acknowledges the path to the Olympic Stadium in Kiev will be challenging, he believes getting there is not beyond the realms of possibility but will need fortune to favour them.
"If we show our quality and have a bit of luck, we can reach the final," Shevchenko told reporters.
"I understand that will be extremely difficult but you only get one chance to make history."
Shevchenko has been an excellent servant to Ukraine, scoring 46 goals in 107 caps over a 17-year spell, but was widely expected to call time on his international career prior to the tournament.
However, he revealed that seeing his country host a European Championship convinced him to prolong his duties with the Yellow-Blues, but insisted he will put their interests first rather than his own.
"For the last five years I've hardly thought about anything but the European Championship that will be held in my country," he continued. "It's fair to say this has extended my career. It's my dream.
"I need more time for rehabilitation. That's natural. If I'm not completely fit I don't want to play and let down the fans. I want to do what's best for the side."
Ukraine prepare for their last warm-up match against Turkey on Monday, before they begin their Euro 2012 campaign against Sweden on June 11.