Sean Dyche described the Sunderland stalemate as a “game of missed chances”.
First half efforts from George Boyd and Ashley Barnes went begging as the Clarets bossed proceedings.
After the break, The Black Cats stepped up their game and Billy Jones missed a glorious chance, before Adnan Januzaj was brilliantly denied by Tom Heaton.
And after sub Sam Vokes saw his late effort well saved by Jordan Pickford, the Burnley boss reflected on another important point to the tally.
Dyche said: “I think it was a game of missed chances. Certainly, in the first half we had two golden moments and a possible penalty for a flailing arm.
“I thought we were really good in that first half and had control of the game, but in the second half they had to come out and they created two really good chances.
“We had that final moment when Sam went through and we thought we were finally going to win that game, but their keeper made a fine save.
“My only real disappointment today is that we didn’t get that lead because you could sense the anxiety and nervousness in the stadium and if Boydy or Ashley gets that touch in the first half it changes the whole feel around the place.
“As it happens, they got to half time and they got a response after the break, so I am pleased overall.
“It’s not easy to go away in the Premier League and it’s another point on the board though and a clean sheet to add to the tally.”
The Clarets have picked up two points from their testing run of four successive away games, to remain eight points above the drop zone.
Dyche added: “A lot was made of these four away games and a really tough run, but we’ve come out of them with two points and could have had more if I’m honest.
“We have to keep working though. We were written off at the start of the season and we’ve got good points on the table so far, but it is only so far, so we have to keep going.
“We’ll have a break now and it’s good to refresh and take stock of the situation before we go into the last nine games, of which we have five at home.
“Overall, I’ve been reasonably happy with the performances away from home. There’s lots of life in us, so now we have to go back to Turf Moor and take on good teams at home.
“It’s easy to forget the journey we are on as a club. We were written off again and here we stand, kind of questioning an away run.
“Overall, you have to say hang on a minute; we’ve got some good points on the table and we’re in good shape.”