The Blues slumped to a 2-1 defeat against Crystal Palace last week.
And the reigning Premier League champions could only manage a 3-3 draw with Roma on Wednesday in the Champions League.
Speculation has been mounting about the former Juventus chief’s future in west London but Conte says he’s still working hard.
He said: “Every coach and manager has to feel the pressure.
“I try to give all myself and put all myself in the job.
“When I go to my house I am happy because I put all myself in the job for fans, club and players. Anything can happen in football.
“At the moment after two defeats and a draw, I am happy for the commitment of my players. After the three results I am not happy.”
Roman Abramovich has owned the west Londoners since 2003 - and isn’t averse to giving managers the boot.
When asked if he has the board’s backing, Conte added: “The most important thing to do is to work, always to have this enthusiasm. I don’t care what happens around.”
