The Cameroon international has not scored since a 2-0 league win over Dynamo Moscow on October 7.
He has seven goals in nine Europa League games for Anzhi though, and Petrovic is hopeful he will rediscover that touch against Liverpool.
"If he don't score in the last few games, maybe he scores tomorrow [Thursday]," said Petrovic, standing in for coach Guus Hiddink who was absent from the pre-match press conference because of a bereavement.
"He's the most important player for Anzhi. If Eto'o plays it's important not just to score the goals but because he gave two fantastic assists in last game."
While Eto'o is the Russian side's marquee big-money signing they are trying to ensure they are able to build for a more sustainable future.
Anzhi, in existence only since the 1990s, have opened a youth academy to grow their own players.
"I am very proud that Anzhi opened something brilliant in Dagestan, a fantastic academy, and that in next years maybe players and big talents from Dagestan will be able to play in the national team."