The Blues have now lost three of their last five games in all competitions without scoring, with Bournemouth and Manchester City inflicting 4-0 and 6-0 defeats, respectively.
Sarri has just six days to try and pick his players up before their Carabao Cup final against City, a game which could prove decisive in whether or not he keeps his job.
And the Italian admitted he was not entirely sure if his players still backed him following the recent run of poor results.
“I think [the players are still with me]. Of course, I am not sure, but I think so," Sarri said after the game.
"I think the situation with the players is really very good for the relationship, but the relationship is not so important.
"It's important to play, it's important to get good results, but my relationship with my players is good at the moment.”
Sarri also voiced his frustration at the lack of fight his players showed - a criticism he has levelled at them before.
“We need all to improve because I am not able to get out of my players a very high level of aggression and determination."
He defended his side's performance as a whole, however, saying that his team were 'unlucky'.
“I think that, with the result, we were unlucky," he said.
"In the first half we played better than the opponent and, at the end of the first half, it was 2-0 to them.
"Then in the second half, it was really very difficult to play because they are a really physical team and defended very low, compact.
"So we played confused football in the second half. But, in the first half, we played well.
"We need, of course, more aggression, more determination in the situation inside our box, and inside the opposing box.
"Because the difference was there. We played 78 balls in the opposing goal, and United played only 16 into our box, and it was 2-0. That was the difference.”