Against a team that had lost each of their previous seven Premier League fixtures this season without scoring a solitary goal, the Blues suffered their second successive defeat and third from eight games in the league.
The latest, following Cesar Azpilicueta's own goal and Wilfried Zaha's first-half finish, means the defending champions have already fallen nine points behind first-placed Manchester City and manager Conte has demanded an instant reaction.
"It will be very difficult for me to sleep," he said. "You know I don't like to lose: imagine when you lose two in a row. My soul is bad.
"We must have the same sensation, me and my players, to change in the next game and be positive.
"(It was) difficult from the start. Our start was poor – you have to start with more personality, otherwise you allow your opponent to take confidence.
"We conceded the first goal, then we were able to come back and, in the last few minutes of the first half, concede another bad goal. Then it was very difficult."
Before their two latest defeats, the first against City, Chelsea had excelled in winning at Atletico Madrid, and Conte admitted midfielder Kante is difficult to replace.
"To lose a player like Kante is not simple because he's able to cover a lot of the pitch," added the 48-year-old Italian. "Our balance was poor.
"Moses is out (on Wednesday) because he's injured (after being substituted in the first half). I don't know if his injury is serious. Kante is still out, and I hope to have Morata back."