The big hero of the match was left-back Ethan Pinnock, who reached the top of a cross and headed in the lead goal in the 58th minute.
Chelsea sent everything up, including the keeper on a corner in the closing stages. But rather than an equaliser, Brentford were able to counter in 2-0 through Bryan Mbuemo.
There is thus a lot left to think about for new Chelsea coach Mauricio Pochettino, who took over after last year’s fiasco season when they finished twelfth.
Championship team Blackburn awaits next in the league cup on Wednesday. Brentford will be rested until Saturday. Then another London derby awaits when West Ham come to visit.