Chelsea ended a run of three games without a win with a 4-2 Premier League victory over Watford on Saturday
Conte's side host beleaguered Everton in the Carabao Cup at Stamford Bridge on Wednesday, and Courtois now believes the Blues can hit back to top form.
"When a top team has a few bad results the first thing people try to say is that the players are not happy and we're not behind the coach, but against Watford you saw we fought for every moment and we fought when we were down, so everybody can see we're behind the coach," Courtois told the club's official website
"Those rumours are easy to spread but I don't think they are true
If somebody is unhappy, instead of going to the press I think they would say it internally, so it's not true.
"First of all, it's the players that have to do it on the pitch so it was important to win, to fight
At the moment it's more running, fighting and battling for every ball than maybe the best football."
Everton sacked Ronald Koeman this week after a run of five games without a win, but Courtois still anticipates a tough challenge from the Toffees.
"It's a cup, and with any cup you want to win it," Courtois added.
"You want to go far
With injuries, maybe we don't have the possibility to rotate a lot so we will have to see what team the manager puts out, but I don't think it's a moment to relax.
"It's a different kind of pressure than the Champions League, where we are doing well and we want to stay top of the group
In the Premier League we have to fight to keep on winning games and the Carabao Cup is something else, so we must try to do our best and go far.
"Everton have been struggling at the moment
I don't think they are playing badly but they have conceded some sloppy goals, and other teams have had more luck, but the Premier League is hard
This is another competition, though, and they will be ready to win it."
Source : PA