Chelsea ended a worrying run of three games without a win with a hard-earned 4-2 victory over Watford on Saturday.
It was a tough match that relied on a tactical gamble paying off, as Chelsea scored two late goals to come from behind and claim a dramatic victory.
“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 Chelsea 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.”
Watford was a challenge and Courtois will hope that Everton will bring an easier game when they visit Stamford Bridge for their Carabou Cup clash with Chelsea on Wednesday.
But the Toffees may be rejuvenated after Ronald Koeman was sacked this week following a dismal run of form that has left them third from bottom of the Premier League.
“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.”