Lewis Dunk gave the Seagulls a 36th minute lead before Johann Gudmundsson leveled for the Clarets in the second half, but the result means the South Coast club took seven points from three games this week.
Here's the most important quotes the Brighton manager made to the media following the match this evening:
Immediate reaction after the match
As Brighton pick up a point from their visit to Turf Moor, Potter hailed the week his side had after victories over Tottenham Hotspur and Liverpool.
"A hard-earned point. A tough game against a good opponent.
"They pushed us all the way and I can't say that we deserved more than a point. It has been a fantastic week for us. Seven points and we move forward."
On playing three games in seven days
The Seagulls have had a busy fixture list and the gaffer was pleased with the effort his side put in, especially as Burnley piled on the pressure in the second half.
"It is the same for everybody but yes from maintaining a performance level it is not easy to do.
"You have to give Burnley the praise they deserve because they put us under pressure in the second half. We hold on for a point and we are happy about that."
On the injuries to Adam Webster and Solly March
Center back Adam Webster suffered an ankle injury and will undergo further assessment while left wing back Solly March is to undergo surgery on the knee injury he suffered in the victory at Liverpool.
"Solly's injury is a big blow for him and us and we wish him well in his recovery.
"It's too early to say for certain about Adam but it doesn't look too bad. He just rolled his ankle. The initial signs are encouraging."