"It was hard to leave them out but it's part of the job," Bilic said. "They are quality players who have done a lot for our side. Unfortunately, they are strikers, the one part of our team where we have the best options so there was simply no room for them."
Klasnic, 32, who underwent a kidney transplant in 2007, had a disappointing season at Bolton Wanderers, while Petric, 31, was also plagued by injuries and poor form at German side Hamburg.
Bilic is likely to pair in-form Everton striker Nikica Jelavic and Wolfsburg's Mario Mandzukic up front. Two other stalwarts, Bayern Munich's Ivica Olic and Brazilian-born Eduardo of Shakhtar, have not played regularly this season.
The 43-year old coach, who took over Croatia in 2006, confirmed he would step down after the finals.
"This is my last tournament. After this, I shall certainly no longer be the national coach. But before that, we must focus on the big job that's coming up," Bilic said.
"I wish my successor all the happiness in the world and hope to leave him some continuity."
He said Ireland coach Giovanni Trapattoni was sticking to tried and tested players and no surprises were likely.
"They are tough, strong, well-organised and defend very well. They only surprise could be if Trapattoni made them more offensive. But that would only make us happier," Bilic said.
Croatia open their campaign in Group C against Ireland on June 10. Also in that group are Italy and world and European champions Spain.
Goalkeepers: Stipe Pletikosa (FC Rostov), Danijel Subasic (Hajduk Split), Ivan Kelava (Dinamo Zagreb); Goran Blazevic (Hajduk Split)
Defenders: Vedran Corluka (Tottenham), Sime Vrsaljko (Dinamo Zagreb), Dejan Lovren (Olympique Lyon), Josip Simunic (Dinamo Zagreb), Ivan Strinic (Dnipro), Gordon Schildenfeld (Eintracht Frankfurt), Domagoj Vida (Dinamo Zagreb), Jurica Buljat (Maccabi), Daniel Pranjic (Bayern Munich)
Midfielders: Darijo Srna (Shakhtar Donetsk), Ognjen Vukojevic (Dynamo Kiev), Ivan Rakitic (Sevilla), Tomislav Dujmovic (Dynamo Moscow), Luka Modric (Tottenham), Milan Badelj (Dinamo Zagreb), Niko Kranjcar (Tottenham), Ivan Perisic (Borussia Dortmund), Ivo Ilicevic (Hamburger).
Forwards: Mario Mandzukic (Wolfsburg), Eduardo Da Silva (Shakhtar Donetsk), Nikica Jelavic (Everton), Nikola Kalinic (Dnipro), Ivica Olic (Bayern)