"We played confused football in the second half, but in the first half we played well", Sarri said (via BBC Sport).
The defeat sees the pressure increase on boss Maurizio Sarri.
There were also signs at Stamford Bridge that fans' patience with Sarri's possession-based style has run out.
"We play Liverpool next week, but Chelsea, Arsenal and us will fight for that fourth position. three good teams fighting for that one position".
Sarri endured chants of "You don't know what you're doing" and "You're getting sacked in the morning" as furious Chelsea fans showed their frustration at the club's fifth defeat in their last 10 games.
Manchester United were drawn away from home for the third round in succession with Molineux their next destination following victories at Emirates Stadium and Stamford Bridge.
But Nevin feels the low expectations from fans after the defeat to Manchester United could work in Chelsea's favour during their games against Manchester City and Tottenham Hotspur in the coming weeks.
Pep Guardiola's side will make another trip to south Wales after beating Newport in the fifth round.
The Italian is now acting as the club's first-team assistant boss and has been since the appointment of former Napoli manager Sarri in the summer.
The Red Devils headed into the game looking to gain revenge on Chelsea FC, after having lost last season's final to the Blues at Wembley back in May.
"Sarri-ball is broken", said Sutton.
Liverpool is now level on points with Manchester City but have a game's advantage.
"To have a successful team you need to have somebody, or some players, who sacrifice themselves for the team".
A source told Telegraph Sport: "Which top manager is going to want to go anywhere near Chelsea at the moment?"