The Blues secured the continental title for the first time in the club's history, defeating Barcelona and Bayern Munich along the way, both of whom were highly favoured.
|7/1||Portugal are 7/1 to win Euro 2012 with Sportingbet|
"I won the Champions League with Chelsea and no one was backing us," he told reporters at a press conference.
"We have to be realistic and think match by match. But it is true that Chelsea's example makes me dream.
"This is a dream that every Portuguese has, but it will be very hard to realise. If we do it, it would be a tremendous feat."
Portugal are tipped to beat Czech Republic in their quarter-final contest, but Meireles has warned his team against underestimating Michal Bilek's men.
"Germany and Netherlands were also favourites in the group and we were able to progress," he noted. "If Czech Republic are in the quarter-finals, it is because they good.
"We have shown that we are a well-organised team, with quality players who can make the difference up front.
"If we continue to play like we have played so far, we have every chance to go through."
After failing to impress in Portugal's first two matches at Euro 2012, Cristiano Ronaldo turned in a world-class display to inspire the Seleccao to a 2-1 victory against Netherlands in their last group match.
"The entire squad has been happy since the first game," the 29-year-old added.
"Sometimes things do not go the way we want, but Cristiano Ronaldo is the best player in the world and our leader."