Manchester United restricted Chelsea to just two shots on target as they dumped them out of the cup by a 2-0 scoreline, inflicting the Blues' third defeat in five games.
However, the Italian says he is not concerned about the chants aimed at him by fans but rather is solely focused on winning matches.
“I am worried about the results. Not about the fans," Sarri said after the game.
"I can understand the situation and our fans because the result wasn't good.
"We are out of the FA Cup, so I can understand them. But I am worried at the moment about our results.”
However, he believes getting the supporters back onside is easily done.
“It's really very easy. If we are able to win three or four matches in a row, it will be very easy. It's difficult to win five matches in a row.”
When asked about the nature of the chants, Sarri was evasive and admitted that his players had not yet completely grasped his 'Sarriball' philosophy.
“Not completely at the moment," he said. "Because, especially in a situation like in the second half, we need to move the ball faster.
"Faster mentally. Faster materially. We need movement without the ball.
"Less individual actions, because when you have spaces, of course, you can go for
Sarri was stoic when asked if he was worried about his job and if he would be given time to turn things around.
“It's not my problem. My problem is to start (preparing) for the game tomorrow morning and to work with my players to try and improve in a few days.
"Find more determination, more aggression, because we conceded the second goal without determination or aggression.
"I was worried when I was in League Two in Italy, but not now.”