Los Rojiblancos come into the Europa League last 16 first leg without a win in five La Liga matches, leaving them ninth in the standings.
Atletico will hope for a change of fortunes when they welcome Besiktas to Estadio Vicente Calderon on Thursday, with Courtois confident they can extend the Turkish side's seven-match winless streak in UEFA competitions in Spain.
"We have five games without a win but we played well," he told the club's official website, www.clubatleticodemadrid.com.
"The first half we played very well in Seville [in Saturday's 1-1 draw]. In the second half, Sevilla were better but I think the point in Seville is good because they are very difficult opponents.
"The feeling is good in the camp, we played very well and we had many opportunities. The wins will come.
"Now we have a very important game against Besiktas on Thursday.
"It is a very difficult game but we have to win at home because we expect to go very far in Europe.
"Besiktas are a good team with experienced players. It will be a tough game, but we must win at home and keep a clean sheet.
"We know at Besiktas' stadium it will be very difficult because they have a very hot crowd so we have to win the first leg."
Courtois is on loan from Barclays Premier League club Chelsea and has been linked with a permanent move to Atletico's rivals Real Madrid.
The Belgian international, though, is only concerned on life with Diego Simeone's side.
"I do not know what will happen at Chelsea, but now the most important thing for me is Atletico Madrid," he added.
"I do not know who the new coach will be but that is not my problem. I want to go another year here because I think it is best for me, but let's see.
"Chelsea know that I want to continue another year, but just wait a bit. They know that Atletico are a good team and the league is good.
"So I think they will decide for me to stay another year here. Now I do not know. In one or two months will be resolved."
Atletico will be without Turkey international Arda Turan due to a recurrent groin injury, while Besiktas will be without Hugo Almeida.
The Portuguese striker is recovering from a knock and has not travelled to the Spanish capital, while Mustafa Pektemek is a doubt for the first leg.