"We have enough quality and depth in the squad to carve out three much-needed points and we are not paying attention to suggestions that this is the worst situation we have been in," Bilic told a news conference on Wednesday.
"I don't have too many doubts about my starting lineup but we are yet to decide whether to deploy the standard 4-4-2 formation or a more attacking 4-4-3," he said.
England top the group with 15 points from five matches, ahead of Croatia with 10 from five and Ukraine, who have seven from four games.
Defeat or even a draw would leave Croatia's bid to qualify for next year's finals hanging in the balance and daily Jutarnji List suggested their position is precarious.
"Bilic's position only seems to be relatively comfortable but in reality, his team is in trouble if Ukraine comes away with anything from Zagreb," it said.
"The fixture list favours the Ukrainians because they play Andorra twice and will be at home to England, while we have to go to Wembley in our final match."
Bilic, who took over in 2006, steered Croatia to Euro 2008 with a flawless qualifying run in which they twice beat England.
But their 2010 qualifying campaign has been hit by a 4-1 thumping by a galvanised England in Zagreb, followed by a 0-0 away draw with Ukraine.
BEST FORM
Bilic said he hoped his goal-shy forwards, particularly Mladen Petric who has not scored for Croatia since their 3-2 win over England at Wembley in 2007, would finally begin to deliver.
"Petric is showing signs of his best form in a while, and I have made it clear to him and other forwards we expect them to fire on all cylinders on Saturday.
"I am sure they will rise to the occasion and it's also a good thing that players battling niggling injuries look like they will be fit."
Bilic's counterpart Olexiy Mikhaylichenko is likely to leave his unsettled striker Andriy Shevchenko on the bench for what he sees as an "important but not decisive" match and hinted his side would play cautiously.
"Our priority is not to lose and show our potential in attack when the opportunity comes, because we have a game in hand and everything is open," he said.
Probable teams:
Croatia: Vedran Runje; Danijel Pranjic, Josip Simunic, Robert Kovac, Vedran Corluka; Luka Modric, Ivan Juric, Ognjen Vukojevic, Darijo Srna; Ivica Olic, Mladen Petric.
Ukraine: Andriy Pyatov; Dmytro Chygrynskiy, Oleksander Kucher, Vyacheslav Shevchuk, Hrihoriy Yarmash; Anatoly Tymoshchuk, Evgen Levchenko, Oleksandr Aliev, Serhiy Nazarenko; Andriy Voronin, Artem Milevskiy.
