Bilic faces a tough task if he is to add Pellegrini's scalp to his belt alongside those of Arsene Wenger and Brendan Rodgers, but exuded quiet confidence in his tried and tested counter-attacking gameplan when he spoke to reporters ahead of Saturday's Premier League game at the Etihad Stadium.
"Man City will feel they need a response after Juventus (in the Champions League), but that won't affect their confidence," the Croatian said.
"Man City didn't deserve to lose that game, minimum they deserved a point, but Juventus scored two great goals," he added.
City have been in blistering form in the league, winning all five of their games so far and smashing in 11 goals, including three against defending champions Chelsea. They are also the only team yet to concede a goal.
They currently top the table and, although Bilic admits they are "cruising at this early stage", he is unwilling to write off his own team's chances of causing another upset.
"We have done it already at Arsenal and Liverpool so we know what we have to do to give ourselves a chance," he said.
One point in Bilic's favour is that West Ham have finally broken their league duck at home, winning 2-0 on Monday at the Boleyn Ground to catapult themselves up to fifth place in the standings and send Newcastle United crashing to the bottom of the league.
The manager confirmed that he would be without the services of defender Angelo Ogbonna for two-three weeks due to a hamstring injury, but said midfielder Pedro Obiang was likely to feature after the knock to his ankle he picked up against Newcastle turned out to be "nothing major".
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
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