A dull 0-0 draw against Denmark in Moscow on Tuesday - the first stalemate of the tournament - ensured Age Hareide's went through in second spot behind Les Bleus.
A lack of cohesion was clear, with Antoine Griezmann and strike partner Olivier Giroud only completing one pass to each other during their 68 minutes on the pitch.
With Lloris on the bench, Real Madrid defender Varane wore the captain's armband and he suggested France will have to find more gears in the knockout stages.
"We had an opponent who wanted to play for the draw," Varane said to TF1. "It was not easy to find rhythm but we are satisfied because we have provided what was necessary.
"We had to be serious and focused. We did not concede many chances, we did not concede a goal.
"We are waiting to see what we are capable of. We will have to raise the level of play. We will be able to see our true potential from now on."
France will find out their last-16 opponents later on Tuesday, with Argentina needing to beat second-placed Nigeria to have a chance of finishing in the top two of Group D.