The loss, coupled with Chelsea's 3-0 defeat at home to Bournemouth last Wednesday, has left the club sitting in fourth place, just a point above Tottenham.
Speaking to reporters after the 4-1 loss, Conte said when asked if he was concerned about his future at Chelsea: "No. It's very difficult for me to transfer my thoughts... I hope that, tonight, for once you understand me. I'm not worried. I'm not worried about my job.
"I work every day, and I give 120 per cent. Okay? If this is enough, it's okay. Otherwise, the club can take a different decision. But I'm not worried.
"It's very difficult because, every day and every press conference, you ask me if I'm worried. No. I'm not worried. Tomorrow is another day. I can be the Chelsea coach or not. Which is the problem?
"My soul [conscience] is clear. I go to sleep without a problem that maybe, maybe, I could do this or that. I try to do everything. If it's not good, the club can make a different decision. Life goes on."