Atletico have lost 3-0 to Rayo Vallecano and Barcelona in recent weeks and Spurs will also have taken heart from their 1-1 draw at Premier League champions Liverpool on Sunday, which ended a five-match losing streak in the league.
Asked whether Tottenham truly believed they could still progress or if they were just hoping to restore their dented confidence with a win, Tudor told reporters: "Both things, it is a game which we should play to pass (progress to next round).
"Our first thing is to stay in the league, but tomorrow is a big challenge to show we can do good things, that they are not better than us.
"It is difficult but not impossible. We need to stay in the game, focus on our strengths. Everything is still to play for, believing we can do it is the important thing from the start."
Gallagher doubtful, Romero returns
The Croatian manager said Tottenham would make a late call on midfielder Conor Gallagher, and that defender Cristian Romero, who suffered a clash of heads with teammate Joao Palhinha in the first leg, was fit again.
"We see today what we can do (about Gallagher). He has asthma problems, maybe some virus, it is not a nice thing. We will see tomorrow if he is fit for the bench," Tudor said.
"Joao is a no, Destiny (Udogie) and Lucas (Bergvall) will be on the bench, but not part of the game too much as they have just come back to us. Cristian Romero is there, he can play."
Spurs players not switched off
Spurs defender Micky van de Ven hit back at speculation over the commitment of the players and dismissed reports of dressing room apathy.
"The other day when we read that one guy had told the rest of the team that he doesn't care because he's leaving anyway. How does this come out? It's just made up," the Dutch international added.
"And the fans will believe it. It's just frustrating for us guys. It brings so much more trouble as well, because fans are starting to believe this.
"But trust me, all the people involved on the pitch, the staff, the players, everyone, they care so much about the situation we're in right now, and we just want to turn things around."