Chelsea boss Mourinho conceded defeat when Bradford’s fourth went in early in the six minutes of stoppage time, offering Parkinson a handshake which the City chief refused.
Parkinson, who later revealed Mourinho went into the visiting dressing room to shake every player’s hand, said: “At that point, there was three-and-a-half minutes left. I wasn’t getting drawn into that.
“Two-goal leads are great, but they can be quickly reduced. We just wanted to stay focused on the result until the whistle went.”
Embarrassed Mourinho branded Chelsea’s exit as “unacceptable” and a “disgrace”.
“I could find in my bad feelings with the game and with the result space to feel happy for them,” said Mourinho. “I also feel ashamed and I think the players should feel exactly the same as I feel.
“But this is the beauty of football, the beauty of the FA Cup.
“I repeat the word that I used in case we lost – it’s a disgrace and it’s unacceptable.”