Clarets boss Sean Dyche felt his side created enough chances to end Brighton's unbeaten start to the season.
Bobby Zamora's first-minute goal was cancelled shortly after by Andre Gray's penalty after Lewis Dunk pulled Michael Keane's shirt in the area.
But Burnley pushed Brighton back for spells, with Rouwen Hennings and Scott Arfield, in particular, going close.
And Dyche said: "I thought they got a very fortuitous start - I've seen it back and every time we blocked it, it seem d to land perfectly for their player.
"I won't be too critical of my players for that, sometime they are the breaks you need to get a goal.
"But our reaction, as ever, was first class, a definite penalty, which is good because we've had a lot not given this season, and then after that, the game was pretty even first half.
"Second half, on chances, we were productive, we had the best chances to go and win it, but they are a good side, they've made a mark for themselves by being unbeaten.
"I'm pleased they haven't really tested Tom, which is a good sign of the defensive framework of the team, and we've opened up enough chances to win the game.
"But it was a very close game between two good sides."
"No disappointments" is the mantra from Dyche and his players, and their reaction to going behind spoke volumes: "The good thing I like about this group is they don't take knocks to heart, they react immediately, and we did.
"We were immediately productive to win a corner, we get a penalty, which you can't guarantee, but the whole feel of the game, I thought we were on the front foot for a lot of the game, and against a good side.
"We lost a player who has been very important to us right at the last minute, which didn't put us out of our stride, which I was pleased with, that shows a good mentality yet again, and I like a lot of what the group did.
"You take your chances, and you win the game.
"Very good play for Scotty to whip one past the far corner, had the crowd on their feet, then the great chance when Andre did well to get into the corner and I will remind everyone, they might question the finish, but it was Scotty getting on the end of his own pass - fantastic mentally and physically to do that.
"Chris Long had a glimmer of a chance with a little toe poke, and their keeper made an unbelievable save in the first half from short distance from Rouwen after good play from George Boyd.
"That's four, and usually four is enough, but it wasn't today."