"Another win, we deserved to win," Conte told Sky Sports. "We played with great concentration against a strong, physical team.
"To win 11 in a row is fantastic. The most important thing is that we are a team, in every moment of the every game. When we suffer we suffer together. I see every day their commitment."
Without being scintillating Chelsea were well worth the win although they offered precious little until Costa opened the scoring. The first-half action matched the gloomy weather but Chelsea went in ahead thanks to a goal of stunning simplicity. Eden Hazard played the ball to Azpilicueta and his dinked cross was perfect for Costa to find the corner of the net.
They will miss his predatory instincts against Bournemouth on Boxing Day, however, after he picked up an early yellow card and a one-match suspension.
Palace were energetic at the start of the second half but could not ruffle a Chelsea defence in total command. The visitors looked the more likely side to score again with Marcos Alonso firing into the side-netting.
N'Golo Kante forced a fine save from Hennessey before Alonso struck the underside of the crossbar with a free kick and Cahill was unable to nod home an inviting rebound. Palace have won only once in their last 11 league games and remained three points above the bottom three.