Paul Pogba's first strike of the tournament and an own goal from Joseph Yobo secured a 2-0 triumph in Brasilia for France on Monday.
Deschamps, who has never lost a World Cup match as a player or coach, is proud of his team's achievement in reaching the last eight but eager to progress further in the competition, with Germany or Algeria set to represent their quarter-final opposition.
"We are part of the eight best teams in the world," he told TF1. "This is a great feeling of happiness.
"I am very proud of what we have done since the start of the competition. Now we have to keep going.
"We had a lot of chances and had control from the 60th minute. There was tension late on because we were in front of a very athletic team.
"We need to savour this win, and in four days we will do it again. We are in the quarter-finals, but this was just another step."
France have now kept clean sheets in three of their four games in the tournament, with Switzerland the only team to find a way past Hugo Lloris in a match Deschamps' men won 5-2.
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