The Frenchman was substituted after only 12 minutes in the match, being replaced by Mason Mount as goals from Anthony Martial and Harry Maguire condemned Chelsea to their ninth defeat of the campaign.
"It's an adductor injury," Lampard told reporters after the game. "We'll have to assess it but it doesn't look great."
Speaking to Chelsea's Fifth Stand app, Lampard confirmed that the 28-year-old will likely miss out Saturday's London derby with Tottenham Hotspur, saying: ""N'Golo, after what happened tonight, is probably a no for Saturday."
Kante has made 122 appearances for the London outfit since his arrival from Leicester City, scoring 11 goals in that time.