The Black Cats are still without a victory in the Premier League this season as they drew for the fourth time, but were unlucky not to snatch a winner late on as Patrick van Aanholt's effort crashed off the post.
Mannone told the club's official website: "The clean sheet is a positive and we defended well today and had spells were we put Burnley under great pressure we just couldn't finish the game off.
"It was a tough game away from home and you know you're going to be tested, they're a newly promoted side and they want to prove they can compete in the Barclays Premier League.
"Overall I think we're disappointed because we know we are a very good side and we should have done better."
Sunderland are 15th in the Premier League after five matches this season.