According to the Daily Mail's Sami Mokbel, he said:
"No, 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 OK.
"Otherwise, the club can take a different decision. But I'm not worried. Tomorrow is another day. I can be the Chelsea coach or not. Which is the problem? My soul 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."
The Mirror's John Cross believes his comments might prompt the Blues to part with him:
John Cross @johncrossmirror
Antonio Conte has just given a very emotional press conference but if the defeat didn't get him the sack then some of his words just might. Said his players are beset by fear, questioned whether they are big enough to play for Chelsea and it felt like he was saying goodbye.
Chelsea played for an hour with 10 men after Tiemoue Bakayoko picked up two bookings in the opening 30 minutes.
Troy Deeney gave the Hornets the lead shortly before half-time from the penalty spot after Thibaut Courtois was somewhat harshly adjudged to have brought down Gerard Deulofeu.
Eden Hazard looked to have salvaged a point when he netted a sublime equaliser in the 82nd minute, but Daryl Janmaat, Deulofeu and Roberto Pereyra all struck in the closing stages to hand Watford a deserved win.
The result leaves Chelsea in fourth and continues their dreadful start to 2018. The Blues won just twice in January—against Brighton & Hove Albion and Newcastle United—and were knocked out of the Carabao Cup by Arsenal, and they've now lost back-to-back games by three-goal margins after going down 3-0 against Bournemouth.
Despite their difficult spell, football journalist Dan Levene demonstrated why the Italian perhaps deserves more time to turn things around:
If Chelsea do decide to pull the trigger, Sky Sports' Kaveh Solhekol can understand why Conte would not be unduly upset:
Having won three Serie A titles with Juventus in as many seasons at the club and guided the Blues to the Premier League title in his first year in charge, Conte's stock should remain high despite their drop-off in this campaign.
Perhaps the only thing missing from his resume is UEFA Champions League success, given he has never reached the semi-finals of the competition, but it's evident he's an elite coach.
The 48-year-old discussed Chelsea's struggles this season and hinted some of the players must take responsibility:
"To play football in a great club, it means you must have a personality because it's simple to play when there is the confidence.
"Especially in this type of moment, you can see who is [ready to play] for a great club. To play with personality and also to risk something."
While it's Conte's job to get the best out of his charges, and it's clear he has often been unable to do that this year, the players' decline in form is revealing a pattern at Stamford Bridge, as Rory Smith of the New York Times noted:
Whatever the Blues decide to do with Conte, this cycle should be a concern for the club, and it perhaps hints at a cultural issue in need of addressing.
It seems unlikely at this point the manager has a long-term future at Stamford Bridge. Whether he makes it until the end of the season will depend on whether the club trust him to deliver Champions League qualification and get past Barcelona in the last 16 of the competition.