Kinsky's first error against Atletico - a slip - led to Marcos Llorente making it 1-0 in the sixth minute, before Antoine Griezmann added a second eight minutes later.
The Czech Republic international was also at fault for Atletico's third goal, gifting the ball straight to Julian Alvarez to finish easily in the 15th minute.
Kinsky had his head in his hands and was taken off less than two minutes later.
He was not acknowledged by Tudor before he headed down the tunnel.
BBC Sport's chief football writer Phil McNulty, who was at the match, said he was not sure he had "ever witnessed anything quite like this".
Former Tottenham goalkeeper Paul Robinson, commentating on the game for BBC Radio 5 Live, said at the time: "I have never seen that on a football pitch.
"It will be soul-destroying for Kinsky. I would not be surprised if he was in tears. It is a difficult thing to handle.
"It is selfish from the manager. He knows he will not be here for long.
"It is clearly for self-preservation and with no consideration for the young goalkeeper. The manager certainly has not helped his case."