The 2018 winners face Poland on Sunday in their last-16 clash having already lost 1-0 to Tunisia in the group stage.
Germany and Belgium suffered surprise early exits while Spain lost to Japan and Argentina were stunned by Saudi Arabia.
France are favourites to progress but Deschamps, who won the World Cup as a player in 1998, remains wary.
He said: "Will there be other surprises? I only believe what I see. Today, even a great nation, if she is not ready, can have unpleasant situations.
"All the games are difficult, last night too. All the teams are good and prepared. The players all play in good leagues.
"This team (Poland) has had to defend in the first three games, defend a lot, and they defend very well. They love it.
"They have a hardcore of players with good experience. There is (Wojciech) Szczesny, (Kamil) Glik, (Robert) Lewandowski and you have to respect what this team does, they deserve to be there. Szczesny was decisive.
"My players know that there will be a response. They have a lot of attacking options to cause problems for the opponent."
The winners will face England or Senegal in the quarter-finals and goalkeeper Hugo Lloris knows France will have to stop Poland's star man Lewandowski at the Al Thumama Stadium in Doha.
"He is one of the best No.9s in the world. He's an important part of this team. It's still a collective, a team that takes great pleasure in defending and enduring. Lewandowski can make the difference at any time," Lloris said.
Poland squeezed through Group C after losing 2-0 to Argentina in their final game with Mexico unable to take advantage.
It is their first World Cup knockout game since losing to Brazil in the last 16 in 1986.
Lewandowski was anonymous during the limp defeat to Argentina, with Poland going through on goal difference, and manager Czeslaw Michniewicz admits they need to provide the striker with better service.
He said: "It's definitely a problem, we played difficult passes in easy situations, we didn't create enough opportunities for Robert.
"Strikers like that, they need to be near the penalty box. If they are there, like in the match with Saudi Arabia, they could score four goals.
"In the match with Argentina, the opponents didn't allow us to do a lot. We need to realise such an opponent as France will dictate the conditions of the game.
"It's very difficult to escape their pressing but some teams have succeeded. In order to take advantage of every team we need to bring the strikers to the right zone, you can't normally score from your own half."