It was a second consecutive draw for the Clarets as they sit second-from-bottom on the Premier League table.
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Parker said afterwards, "I thought we were worthy of more. We came here understanding what we needed to be - and we were every bit of that.
"I’m frustrated because we didn’t win the game, but the positive is that there was a lot to like about our performance.
"I can’t be critical - we were dominant and deserved more. It’s a point, it’s a clean sheet - and we’ll take it into the next one.'
"We missed a few gilt-edged chances. I think we had over 15 shots over the course of the game.
"That’s the fine margins of the Premier League.
"On another day we take those opportunities and we leave with three points to show for our efforts."