The Croatians were seconds away from clinching a semi-final berth before losing the clash in Vienna on penalties, having taken the lead in the final minute of extra-time.
The Turks equalised with the last kick of extra-time and then won the shootout, as Bilic and Croatia's disconsolate players - most of whom are still in the squad - buried their heads in the grass.
"That match did not have a good ending for us but we were the better side and hence I am optimistic ahead of our Euro 2012 play-off," Bilic told reporters in Croatia's Catez training camp in neighbouring Slovenia on Wednesday.
"Revenge is an ugly word and I don't want to use it because the Turks won fair and square, they didn't cheat their way into the semi-finals.
"They scored a brilliant goal and showed their character so our motive is to qualify for Euro 2012, not revenge.
"As much as we can't get the 2008 defeat out of our system, we will enter the play-off with cool heads and approach it as if it's a cup final with no return leg," Bilic said.
"We always produced our best performances under the greatest pressure and I am convinced we can do the same now, there is no fear among the players because they are used to performing on the big stage."
Since they gained independence from the former Yugoslavia in 1991 the Croatians have qualified for six out of eight major tournaments, missing out only on Euro 2000 in the Netherlands and Belgium and the 2010 World Cup in South Africa.
The highlight of their impressive record was reaching the 1998 World Cup semi-finals, when Bilic was an automatic starter in the centre of Croatia's defence.
The 43-year old coach, under fire from Croatian media after patchy performances in the Euro 2012 qualifiers, acknowledged his job might depend on the outcome of the play-offs.
"I am not thinking about my future because I am completely focused on the two games ahead," he said.
"[Turkey coach Guus] Hiddink is under pressure too, it's part of the job and coaches who are not prepared to accept that are in the wrong business.
The home fans in the Turk Telekom Arena in Istanbul are likely to create an electrifying atmosphere, and the Turkish Football Federation has distributed free tickets to women and children as part of a campaign to root out hooliganism from Turkish stadiums.
Hiddink is likely to field his preferred 4-3-2-1 formation with Trabzonspor's in-form striker Burak Yilmaz up front, while Mehmet Topal and Arda Turan should operate on either flank.
Turkey: Volkan Demirel; Gokhan Gonul, Servet Cetin, Egemen Korkmaz, Hakan Balta; Emre Belozoglu, Selcuk Inan, Hamit Altintop, Mehmet Topal, Arda Turan; Burak Yilmaz.
Croatia: Stipe Pletikosa; Darijo Srna, Domagoj Vida, Josip Simunic, Danijel Pranjic; Ivan Rakitic, Ognjen Vukojevic, Luka Modric, Iv
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.