Diego Costa scored the winner for Cech's former side shortly after Per Mertesacker was sent off at the Emirates Stadium.
And the Arsenal goalkeeper was frustrated to have lost but commended his team's effort - and urged fans to keep going.
Disappointed with the result... Great team effort and attitude down to 10 men ... plenty of points to play for ! Let's keep going! #COYG— Petr Cech (@PetrCech) January 24, 2016
The loss was a bitter one for Arsenal supporters but, despite Chelsea being nearer to the relegation zone than the top four and the Gunners sitting near the top of the Premier League table, it wasn't all that surprising.
Indeed, the Blues traditionally beat Arsenal. That just seems to be fact.
Arsene Wenger's poor record against Jose Mourinho didn't come into play here - but Guus Hiddink seems to overcome him while in charge of Chelsea, anyway.
A disappointing day for Cech and Arsenal, then, although their monthly meltdowns might not be so costly this season if others keep dropping points, too.