The home side had 76 percent possession, 34 shots and hit the woodwork twice as France failed to win against Luxembourg for the first time since 1914.
"It is infuriating to have so many chances and not score," said Deschamps.
"It's a day of glory for Luxembourg football," his counterpart, Luc Holtz said.
Despite playing the team ranked 136 in the world, Deschamps fielded a strong side for the World Cup qualifier in Toulouse, including Manchester United midfielder Paul Pogba, Atletico Madrid forward Antoine Griezmann and Kylian Mbappe, who recently joined Paris St-Germain on loan from Monaco with a view to a £166m transfer next summer.
Griezmann did smack a 30-yard free-kick off the bar five minutes before half-time while Pogba saw a header rebound off the frame of the goal late on.
It could have been worse for Les Bleus, though, as Luxembourg substitute Gerson Rodrigues outpaced Laurent Koscielny in the 79th minute before seeing his shot strike an upright.
France, who beat the Netherlands 4-0 on Thursday, stay top of Group A after the stalemate, although their lead over second-placed Sweden is now just one point.
"Thursday's result was important but so was getting three points [against Luxembourg], so we'll need to fight to the end," Deschamps told TF1.
"The last two games will be decisive. We are in a better situation than we were in June, although we are disappointed tonight."
Luxembourg beat Belarus 1-0 on Thursday for their only win of the qualifying campaign so far.
"We are satisfied with the point, which we got playing with a lot of heart, commitment and also success," added Holtz.
"With a bit more luck we would have got the three points. For Luxembourg, the result is historic. A point against a top team is extremely rare," he added.