The Argentina midfielder captained the side in the absence of Reece James and was seen facing the away end at full time alongside head coach Liam Rosenior, who was also witnessed apologising to supporters before tearing into his players in his post-match interviews.
Goals from Ferdi Kadioglu, Jack Hinshelwood and substitute Danny Welbeck completed a comfortable Brighton victory that sent the hosts above Chelsea into sixth in the Premier League.
The away end directed chants at both the ownership and Rosenior throughout the second half as Chelsea failed to register a single shot on target and produced their fifth consecutive league defeat without scoring — the first such run since 1912.
Rosenior did not hold back afterwards.
"I keep coming out and defending the players — that was indefensible, that performance tonight," he told Sky Sports.
"The manner of the goals we conceded, the duels we lost. Something has to change drastically right here, right now.
"Tonight was not tactical. This was about desire, spirit, courage and I did not see enough of that tonight. I can't come out and lie. That was an unacceptable performance at every level."
Cole Palmer, Estevao Willian and Joao Pedro were all sidelined through injury, but Rosenior made clear that excuses were not available to him or his players.
Chelsea are now seven points behind fifth-placed Liverpool with a game played more. Sunday's FA Cup semi-final against Leeds at Wembley gives the squad an immediate opportunity to respond.