Out of form and regularly conceding goals, Iceland were expected to lose against the World Cup champions, but strikes either side of half-time from Birkir Bjarnason and Kari Arnason put France on the back foot and in danger of a 2-0 loss.
Les Bleus fought back, however, to level the game at the Stade du Roudourou in Guingamp thanks to an 86th-minute own goal by Holmar Orn Eyjolfsson and a last-gasp penalty from substitute Kylian Mbappe.
Deschamps acknowledged his team had got off to a bad start, with Iceland’s organisation seemingly catching them off-guard.
Quoted on the team’s official website, he said: “We started badly in this match, there was a problem with our attitude.
“We were a little too relaxed in front of a well-organised team that played well against us.
“But as soon as we found a little more rhythm, more density, more races forward, we hurt more, but we’re not going to worry.”
Dimitri Payet, Thomas Lemar and Mbappe were among those introduced from the bench but Deschamps maintained he had chosen the right squad.
“It was logical to give playing time to other players, there are two matches,” he added.
On the back of a 6-0 defeat against Switzerland and a 3-0 loss to Belgium, Iceland manager Erik Hamren remained optimistic despite the setback in clinching his first victory.
Quoted on Icelandic site Visir, he said after the match: “I’m proud of the team. We had talked about having a better attitude, tried to work on the defence, we needed to improve after Switzerland and Belgium, the attitude was fantastic to see.
“This is what I wanted to see in our team. Iceland has done it against good teams before and I wanted to see it myself. Now we know what to do – I hope this continues, especially the attitude that the players showed tonight.”