With Liverpool and Paris St Germain also in the section along with debutants Red Star, Ancelotti - who won two Champions League titles in charge of AC Milan and one at Real Madrid - said his Serie A side could not afford a slip up.
"It is a very tough group and therefore it is imperative that we make a good start because we all know how tough it is for visiting teams here," he told a news conference on Monday.
"We also know that Red Star played very well in the Europa League last season and are dominant in the Serbian league, hence we will head into the clash with the utmost respect for them.
"We want to do well in the Champions League this season because it's a great competition and I know my players too will be galvanised by the atmosphere in Belgrade."
Red Star warmed up with a 6-0 Serbian league win over 10-man Radnik Surdulica on Saturday to stretch their perfect start to seven wins, having knocked out Salzburg on away goals to reach the Champions League group stage for the first time.
Although the current crop of players are a far cry from the generation which lifted the European Cup, Red Star coach Vladan Milojevic was confident his unfancied side could give Europe's heavyweights a run for their money.
"We are not here to just make up the numbers, and heading into every match against Europe's finest devoid of any pressure can only play into the our hands," he said.
"We know who we are up against but we have come this far and don't want to stop here. With all due respect to Napoli, we fear no one and the fans can put extra wind in our sails."
Only about 1,000 Napoli fans are expected at the Rajko Mitic stadium, whose capacity is 55,000. Tickets for Red Star's three home group games sold out in just a few hours last Monday.
(Writing by Zoran Milosavljevic; Editing by Ken Ferris)
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