Bakayoko's red card — for two bookings in just five minutes — put the Premier League champions on the back foot, with Troy Deeney converting a penalty to put Watford ahead before the break.
Chelsea eventually mustered a response thanks to Eden Hazard's fine finish, but a late flurry of goals from Daryl Janmaat, Gerard Deulofeu and Roberto Pereyra wrapped up Javi Gracia's first Hornets win.
Conte's men were dire in a 3-0 home loss to Bournemouth on Wednesday but this performance was as bad if not worse, leaving the Italian to accept he picked the wrong team.
"To play football in a great club it means you must have a personality, because it is simple to play when there is the confidence," Conte said during a post-match press conference.
"Especially in this type of moment it is simple to see who. In this moment you have to show and have personality
"For sure I have to take the responsibility as maybe I made the wrong decision with the starting eleven.
"We played without personality, from the start I didn't see confidence to play football. Usually we train and play with confidence and take the risk, but today we started very poor and with fear and this is the worst situation for a coach."
3 - Chelsea have lost consecutive Premier League games by a margin of 3+ goals for the first time since October 1995 (1-4 vs Man Utd and 0-3 vs Blackburn). Humbled.— OptaJoe (@OptaJoe) February 5, 2018
Conte spoke pre-match of desiring a statement of support from the Chelsea board amid continued speculation about his future.
But the 48-year-old did not hold back in his criticism of a performance that made a mockery of Chelsea's status as Premier League champions.
"I have a great disappointment, our performance was very bad," Conte said. "We started poorly without personality, with the fear.
"We are not used to playing this way. We can lose but we always try to play football and be positive. The double yellow card did not change it but the situation became serious. Then there was the penalty and when you go 1-0 down it is difficult to come back with 10 men.
"In the second half we showed good determination but confusion. You have to manage the situation, to understand it. But in 10 minutes we conceded three goals. In this case it is right everyone to take the responsibility — me, the players."