Kante will miss Chelsea’s Premier League clash with Newcastle on Saturday after the midfielder suffered a groin injury last week.
The 28-year-old sustained the problem while warming up for France’s Euro 2020 qualifier with Iceland on Friday.
But instead of being allowed to return to London to be assessed by Chelsea’s medical team, Kante stayed with the France squad and watched from the bench when they faced Turkey the following Monday.
Lampard is unhappy that Deschamps and the French Football Federation failed to let Kante leave.
“N’Golo’s not fit, he had a small groin issue in the warm-up to the first international game for France,” Lampard told reporters on Friday.
“We didn’t get him back until after the second game and he’s not fit for Saturday.
“After the first game when he pulled out, he then had a fitness test the day before the second game, it was clear that he couldn’t play.
“He then sat on the bench on the evening of the game, so that’s not communication.”
Deschamps had previously risked angering Lampard by suggesting Chelsea’s France forward Olivier Giroud is not getting enough playing time at Stamford Bridge.
But Lampard was far more frustrated with the communication breakdown over Kante, who was also unavailable for France in September because of an ankle injury that sidelined him for four Chelsea games.
“Before the international break, I know Didier Deschamps mentioned in jest a little bit about Olivier Giroud and that was obviously quite light-hearted and I get it, we all have our selection problems and he had his in the two games,” Lampard said.
“But the Kante one was not a laughing matter because we communicated before the last international break he was injured so couldn’t go.
“Let’s think what benefits the player, he didn’t go, we both agreed on that. That’s how things should work.
“I understand when players are on international duty they are their player as such, but it was quite clear he wasn’t fit to play.”
– Christensen blow –
Lampard suffered another injury blow this week, with Denmark centre-back Andreas Christensen ruled out for a fortnight.
“Andreas Christensen has got a hamstring injury which will see him out for probably the next two weeks,” Lampard said.
Four of Lampard’s players — Ross Barkley, Tammy Abraham, Fikayo Tomori and Mason Mount — were with England in Bulgaria on Monday for the Euro 2020 qualifier that was twice stopped due to racism from the home fans.
Lampard, who was part of the national team during a previous trip to Bulgaria marred by racism, said he was pleased with the way England dealt with the toxic atmosphere in Sofia.
“I kind of remember the game (in 2011), I think I was on the bench. I felt what we all felt at the time and maybe we did not speak up enough,” he said.
“I think the big progression of Monday night is that the governing body have to take a big step.
“The way the England players and staff dealt with it was really positive. I have spoken to the players, there is not much to say. I am there to support them.”