LA Galaxy striker insists the Boys in Green are not there to make up the numbers and are aiming to qualify from the group despite tough fixtures against Spain and Italy to follow
The LA Galaxy forward knows how crucial a win could be against Slaven Bilic's side with tough group games against Spain and Italy to come.
Giovanni Trapattoni has already named his starting XI for the game, and having remained undefeated for their last 15 games, the Boys in Green are full of confidence.
Keane told reporters: "It's [winning against Croatia] vitally important. Of course in any competition, you want to start off straight away as well as you can and try to get points on the board because we know that in the group, anybody can beat anybody.
"We just have to take each game as it comes, as we always say. We will focus on Sunday's game and see what happens after that.
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"Hopefully we will be talking after that game with three points in the bag."
Ireland qualified for the tournament having lost just once and the 31-year-old is determined to lead his team out of the groups stages and Keane feels they can cause a few shocks at the Championship.
When asked if Ireland could match Greece's 2004 achievements, he added: "I hope so; I certainly hope that's the case.
"Listen, we are not coming to this competition to make the numbers up. We are here to do as well as we can for the country and hopefully go as far as we can.
"We go into every game in every competition believing that we can win it."