Chelsea started well amid difficult wintry conditions at Turf Moor, though, and took the lead after just seven minutes when Pedro finished off a fine counter-attack.
But Burnley rallied well and drew level through Robbie Brady's delightful free-kick just before the half-hour mark and could have even won it if Matt Lowton or Andre Gray had been more composed.
"Burnley away with their home record is a really difficult side to play against," Courtois told Sky Sports, after Chelsea opened up a 10-point gap at the top of table.
"The pitch was not so good with the cold and snow, so it was not an ideal situation.
"But I think that we conceded a free-kick and Brady showed his quality with the goal.
"We couldn't find our game again and slipped - we couldn't find space between the lines and maybe we were a bit sloppy in the end.
"We didn't really have many more chances. Maybe in the end in that situation we are happy with a point."
Courtois felt helpless when trying to keep Brady's free-kick out and accepted that he was beaten by a brilliant strike from the Irishman, who was making his home debut.
"I got a finger on it but not enough," he said. "You can try to anticipate, but if it is a fantastic free-kick with pace into the top corner then it is so very hard to keep out."