That Serie A result delighted the club's supporters but Europe's premier club competition will be a different challenge.
"We played against the strongest team in Serie A in terms of squad potential and we won without playing at our best. That should make us reflect on our real value and what we could have done better," Tudor told reporters on Monday.
"Champions League is a different tournament, it’s beautiful and fascinating. In my experience as a coach, players forget about tiredness in the Champions League. Everyone’s goal is to play. It’s a privilege."
Dortmund, the 2024 Champions League runners-up, have started the Bundesliga season strongly with two wins and a draw.
"They are a great team, not only in Germany but also on the European stage," Tudor said.
"We can’t wait to start this wonderful competition. How far can we go? We’re not thinking about that right now."
The question remains whether 20-year-old Kenan Yildiz will start after his stunning goal against Inter, and Tudor played down comparisons with Juve legend Alessandro Del Piero.
"Let him enjoy his football and grow in peace," the coach said.
Tudor also paid tribute to the quality of his players.
"I’m lucky because I coach a team of serious, focused guys," he said.