The Clarets battled back from 3-0 down to level by the hour, only to lose to Mikkel Damsgaard’s 93rd-minute winner.
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Two late goals were also ruled out by VAR in a thrilling, topsy-turvy Premier League clash.
"We can be critical of the first half, of course we can. We gave ourselves a mountain to climb,” Parker told the media.
"We looked soft in the first half - we lost duels and we were second best for large parts in a difficult environment.
"I could see the hurt in the players eyes at half time with what they went through in the first half.
"But our reaction in the second half - the fight and the spirit - was incredible."
