Giovanni Trapattoni's side failed to earn a point in their three group matches in Poland and Ukraine and the hurt from that is still showing, according to the Stoke forward.
They face a key double-header against Sweden (Friday in Dublin) and Austria in the next week, the two teams they are tied with on 11 points behind Group C leaders Germany.
Walters said: "After the disappointment of the Euros, being there and being so disappointed to go out like we did, you want to get straight back into it.
"Once you have a taste of it, you want to get back in, so everyone is determined to get to Brazil.
"We are all really hungry for these two games and they are going to define where we are going to end up in the group, so they are exciting games to play in.
"You go into every game trying to win. Obviously, the emphasis is on us because we are at home in the first game against Sweden.
"But after that result, whatever it may be, you take each game as it comes, so we will see where we stand after that game and going into the last few games.
"It would be nice to get two wins, and that's what we will probably be aiming for, but we will see where we are after the game."