The Clarets were beaten 2-0 at Turf Moor on Sunday.
Cullen later said: "We can be pleased with a lot of the parts of our game but the overriding emotion is bitterly disappointed we haven't got anything to show for it.
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"We started the game really well, we were on top and creating chances but one chance for them and you get punished. We are learning the hard way.
"After last week we had to show a bit of fight and spirit today. I think we did that. The desire and spirt was there.
"Every decision that has been a close one this season seems to go against us.
"We won't stop fighting until the day is done and there's still enough points left to get us out of this situation."