Sean Dyche happy to see the Clarets find a way to win once again
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The visitors recorded the only shot on target with a minute of normal time remaining, which resulted in the match-winning moment.
Jay Rodriguez, who had replaced Ashley Barnes with a quarter-of-an-hour remaining on the South Coast, leapt above Simon Francis and Jack Stacey to plant Ashley Westwood's delivery in to the corner.
"I am certainly pleased with the result but we can certainly perform better," said the Burnley boss.
"It was a very hard game in that the conditions were awful and the game wasn't much better.
"But we have come out the right side of it and that is a really pleasing thing. It is pleasing in the sense that we have found a way because we have had to do that before and we will have to do it again."
For the second game in succession, and the second time in their Premier League history, the Clarets denied their opposition a shot on target.
Jefferson Lerma failed to threaten Nick Pope's goal in either half while Chris Mepham's header travelled the wrong side of the upright as the Clarets held on for a seventh clean sheet of the campaign.
"You have to find a way and we did," said Dyche. "It was fading away to an ugly game and a 0-0 draw which happens and then we nick it out of a moment of quality that we found when we weren't really finding it.
"In the first half I didn't think there was much in it but in the second half they had the better feel of the game but I can't really remember them opening us up too much.
"There were a couple of flashes across the box and a couple of crosses but not much. It was an odd game, lots of niggly things and low level fouls for me, things I didn't think had much in it - for both sides.
"Credit to them for bringing the game on in the second half but we found a way to get an ugly win and they are as valuable as anything in this division.
"I thought we were better against Newcastle but from a manager's point of view, forgetting about entertainment, what are the fundamentals of a team?
"One is defending properly and stopping the opposition and I thought we did that very well. And two is to find a moment and we did and that is sometimes the way it is."