Les Bleus impressed during their unbeaten group phase, but will look to reach the quarter-finals when they take on Nigeria in the last 16 today.
"We've never been favourites, even though we have produced some beautiful football," Ligue1.com quotes Lloris as saying. "The real World Cup starts now.
"We're just taking each match as it comes and hoping to come out of Monday's clash with the win. We're young team but we have several senior players with a lot of experience. The most important thing is our frame of mind."
Didier Deschamps's side scored eight goals and conceded two as they finished at the top of Group E.