Arsenal midfielder Ozil played the full 90 minutes as Germany slipped to a 1-0 defeat to Mexico in their Group F opener – the side's first competitive defeat since their semi-final exit from Euro 2016 when they lost 2-0 to France.
Effenberg questioned Germany head coach Joachim Low's decision not to include second-half substitute Marco Reus in his starting line-up, calling for the Borussia Dortmund man to be in from the outset against Sweden.
"If what Reus said after the game, that he was earmarked for the 'important games', is true, then the coach has completely misjudged this.
"The most important game was that against the strongest group opponent: Mexico."
Effenberg also called for Ilkay Gundogan to be drafted into the team to help Toni Kroos, who he said was marked out of the game against Mexico.
"The key to Mexico was that Kroos was taken out of the game with man-marking," added Effenberg. "He could not play with his usual rhythm.
"Khedira would have had to help Kroos in this case, take over the role and make the game fast, but he didn't do that. Therefore, the logical consequence would be that he no longer plays against Sweden, as they will do that in a similar way.
"In place of Khedira, Ilkay Gundogan should play. The team simply needs dangerous balls from the central area to the top - that was completely missing against Mexico.
"Gundogan is a player who can play such passes."