The Croatian coach replaced the visibly distressed keeper in the 17th minute on Tuesday after the Czech conceded three goals inside the opening 15 minutes, having slipped trying to clear for the first and miskicked playing the ball out for the third.
"Before the game it was the right choice to do, considering the moment we are in," interim manager Tudor told reporters in a press conference referring to his decision to start 22-year-old Kinsky in place of regular keeper Guglielmo Vicario.
"In this moment we are fragile, we are weak," he added.
It was the hapless Kinsky's first appearance since October and only his third of the season.
Tudor, who has lost all four games since he took charge of Spurs in late February after being sacked by Italian giants Juventus, said his job security was not a topic for him.
Diego Simeone's Atletico, who are firmly on course for the last eight, head to London for the second leg next Wednesday.
"We managed to make the most of their mistake with our pressing," Atletico's Argentina striker Julian Alvarez, who scored twice, told broadcaster Movistar Plus.
"We know what this competition is like. Every detail counts. It's not going to be easy, but we want to be in the quarter-finals," he said when asked about the second leg.