Chelsea midfielder Kante told the Evening Standard that Didier Deschamps's men have faith in their ability to progress deep into the finals.
"We don't feel too much pressure," the 27-year-old said. "We all knew before the competition that we have a good squad and we want to give our best.
"We didn't feel too much pressure. We just wanted to give our best for the next game and the last 16. We deserve first position because we had three good games."
Speaking about Tuesday's draw, Kante added: "We both knew we needed a draw to go through. We played against a very well organised Danish team, very compact, and I think that's why we did not have many chances."
Denmark will play Croatia in their first knockout tie on Sunday.