Spurs travel to Spain sitting 16th in the table, just one point above the relegation zone, after losing all three league matches since Tudor replaced Thomas Frank. The Croatian admitted the domestic situation could not be ignored.
"Our first aim is the Premier League; this should be said publicly, it's a normal thing," Tudor told reporters. "This competition is something extra, but that doesn't mean we don't want to pass through, that we don't want to go to the next round."
Tottenham go into the tie on the back of five consecutive Premier League defeats, a run that has increased the pressure around the club. Tudor, however, believes facing Diego Simeone's experienced Atletico side could help his team reset mentally.
"We're playing against a team that has a story in this Champions League, they have experience, they have quality," he said. "We need to do our best in terms of that we need to grow.
"A totally different mentality aspect can be used in this kind of game. Maybe this can help us to see which problems we have."
Between the two European legs, Spurs face a daunting league trip to Liverpool, before hosting Nottingham Forest in what could prove a decisive clash near the bottom of the table.
Tudor admitted change would take time after less than a month in charge.
"Sometimes old habits take more time than expected to change," he said. "It's not easy to change the things you're doing for months or a year. Something is moving."
In terms of team news, Djed Spence was declared fit, while Cristian Romero returned from suspension. "I'm sure tomorrow he'll be a leader like he always is," Tudor added, underlining the importance of experience as Spurs attempt to steady their season.
Vincent Kompany has remained cautious over Harry Kane's fitness ahead of Bayern Munich's crucial UEFA Champions League Round of 16 clash against Atalanta on Tuesday night, insisting a final decision will be made on matchday morning.
Hansi Flick has insisted Barcelona will not abandon their identity when they face Newcastle United in the Champions League on Tuesday, warning his players to expect a dangerous and highly motivated opponent.
Arne Slot has said Liverpool's previous experience in Istanbul would help his players handle the "very impressive" atmosphere when they face Galatasaray in the UEFA Champions League last-16 on Tuesday night.
Nuno Espirito Santo has praised his players and supporters after West Ham United defeated Brentford on penalties to reach the quarter-finals of the FA Cup following a dramatic night at London Stadium.
