Conte is enduring similar difficulties in his second campaign at Stamford Bridge.
But Courtois told the London Evening Standard: “We are ready to fight for the coach.
“I remember what happened two years ago under Jose Mourinho and things started to be said, there were stories about the dressing room without knowing what was happening.
“We are happy to show that we are ready to fight. We all know what would have happened [more debate over Conte’s future] if we had lost against Watford.
“There was a moment when we were 2-1 down, we were having difficulties and Watford could have made it 4-1. It was very important to come back to win.
“In 2015 [under Mourinho] we wanted to fight as well but the game didn’t turn out well for us, there was too much bad luck. Sometimes different things happened.
“But we are showing we want to fight again now, firstly as a group of players. We want to win games.
“We don’t want to lose and say we don’t care any more. We want to fight for ourselves, too. It is important for us.
“Some of us remember what happened two years ago and we don’t want the same thing to happen.”