Lloris believes football is a team sport and Mbappe should not be singled out for Les Bleus’ elimination.
France were one of the favourite teams to win the tournament but could not beat a spirited Switzerland side, who were determined to cause an upset.
The game needed to be decided on penalties after a thrilling 3-3 battle through 120 minutes from both sides.
The former Monaco man saw his spot kick saved by Borussia Monchengladbach man Yann Sommer, giving Switzerland the 5-4 shootout victory.
"In football, we win together and we lose together," Lloris told beIN Sports when asked about Mbappe.
"We're all responsible for the elimination. It's painful and there is no one to point the finger at. We all fought together against the opponent and there is no excuse to seek. And we have to highlight the Swiss team, they were great."
He added: “I think the regrets we may have are certainly that we could have managed the game better at 3-1. Our strength in the past was to be strong. And we left them in the game.
"Despite that, we didn't give up. We went to the end of the end. Now we have to digest our pain."
