Juve won thanks to an injury-time winner from youngster Vasilije Adzic.
Afterwards, Tudor said: "It was a strange match with so many goals and so many changes in the scoreline. In the end, this shot from Adzic decided the match.
"He's a strong player, and we had the idea of playing him. It's a great victory, because it came against a great team. Before the match, I saw too many exaggerated judgments about Inter.
"We could have done better, and I wanted to press higher and keep the ball better. But we had some players with post-international issues. The first game after the break is never a good one. We wanted to win this game, and the guys felt they could win it."
On if the win proves Juve's title credentials, Tudor also said: "For me, it doesn't matter. There are so many opinions, and that's also what makes football beautiful.
"There's always room for improvement. We're a living organism and we can never be the same. We're on a good path, and this win can give us confidence, and in two days we need to confirm that. We need to go strong right away."