Speaking after the clash at the Santiago Bernabeu, Tudor felt his side's performance warranted at least a point.
Jude Bellingham’s solo effort in the second half proved decisive, maintaining Real Madrid’s 100% record in this season’s competition while leaving Juventus rooted to two points from three matches.
"I'm disappointed we didn't get a point, because we deserved at least one goal," Tudor told reporters. "The lads are disappointed. We had a good approach and the desire to go for it, then it was right to suffer. It's a shame we didn't put the ball in the net."
Juventus, whose last victory came on September 13, showed flashes of promise, with Real goalkeeper Thibaut Courtois making three crucial saves to deny the Italian side's efforts, but were undone by Bellingham’s strike in the 57th minute.
The goal was created by Vinicius Jr, who took on three Juventus players and made space to shoot. His attempt, described as a blend of brilliance and fortune by Tudor, rebounded off the post for Bellingham to slot home his first goal of the season since returning from shoulder surgery.
"It was down to individual skill, because he managed to shoot between three players, and also a bit of luck," Tudor said. "If no one made any mistakes, if things like that never happened, all matches would end without any goals."
Despite the defeat, Tudor remained optimistic about his team’s trajectory, urging patience and belief.
"We have strengths and weaknesses, and we need to have faith because we're on the right track," he said.
"We were definitely missing a bit of everything. The desire was there, but when you run a lot, you also lack a bit of clarity and the habit of playing at certain levels."
Juventus will be aiming to snap their winless run on Sunday when they face Lazio in Serie A, where they sit seventh in the standings, four points behind leaders AC Milan.