The Blues missed a golden opportunity to move up to third after a frustrating night at Stamford Bridge, which saw four goals inside the opening 24 minutes.
Two quickfire goals from N’Golo Kante and Gonzalo Higuain quickly cancelled out Jeff Hendrick’s stunning opener, before Ashley Barnes ghosted in to draw Burnley level.
The hosts bossed possession for the remainder of the game, but they failed to seriously test Burnley goalkeeper Tom Heaton, who was booked for time wasting in the first-half.
And Luiz was not impressed with the visitors’ approach.