Michy Batshuayi came off the substitutes’ bench to score twice against Marco Silva’s men, who led 2-1 early in the second half and missed two huge chances through Richarlison, before Chelsea’s late fightback.
The win came from back-to-back defeats in the Premier League, which had put Conte’s position in doubt.
When it was suggested that under previous managers, the team might have collapsed at 2-1 down, Conte said: “I am not like the previous managers. I am different. It is important to understand this.
“The club has to judge the work and honestly, I don’t have this type of worry [about] if I lose the game, if the club decides to sack me.
“In the past, the club decided after two losses or three bad games to sack a manager. I don’t think it is the same for every manager. You change the person, change the work. I repeat: If you ask if I feel this type of pressure, it is zero.”