Sean Dyche felt the Clarets deserved a reward from their agonising 2-1 defeat at Liverpool.
Ashley Barnes seventh minute opener was cancelled out by Georginio Wijnaldum’s equaliser with the last kick of the first half, before Emre Can rifled home a winner just after the hour mark.
Barnes and Matt Lowton both had good chances to level matters up again, but to no avail as the Clarets went down to another away defeat to the odd goal.
Boss Dyche said: “It’s a tough one to take today. The performance was very good and the shape and endeavour and framework of the side was very important because they are a good side.
“They get bodies forward and they play quickly on the counter, but I thought we dealt with a lot of what they had to offer very well.
“It was a big thing for us to be brave in our performance. We want to go after teams and take on these challenges and today was back to what we are.
“We put the ball in the ball box a lot deliberately to make them uncomfortable and I thought that worked really well and we are scoring away from home regularly, which is another key factor, so there’s a lot to be pleased about.”
Barnes netted the first Burnley goal at Anfield since 1975 early in the game, expertly converting Lowton’s magnificent ball in behind the defence.
Dyche added: “It was a sublime goal from us and to go in 1-1 at half time was unjust, I felt. We were a bit unlucky to be fair because the ball hits Ben (Mee) in the stomach and it lands perfectly.
“That changed the whole feeling in the stadium. That was the really annoying part about it, because I think we all sensed they were going to get a bit of stick going off at half time.
“I was just very pleased with the performance in general, but we’re still looking for that first win and we’ll keep working for it.”
He added: “Our fans were terrific again today because they could get disgruntled. They stick with us unbelievably well and I think them for that because they are travelling everywhere and getting behind the team.
“If the players keep delivering that type of performance, things will break for us because our away performances have definitely got stronger.
“We are coming to places like Anfield and scoring and creating chances. We’ve created three or four really big chances today, so there are a lot of good things and the mentality and the overall feel of the side and the link with the supporters is all intact and we have to take that forward into our last 10 games.”