Mats Wieffer struck twice for Brighton's 2-0 win at Turf Moor.
Parker admitted afterwards: “It’s another frustrating afternoon. I didn’t think there was much in the game.
“The fine, fine margins once again with the two VAR calls - and conceding two goals at the wrong time.
“It felt a fairly even game, but that familiarity of us not making the most of our chances and them being clinical when it mattered most, made the difference.”
Parker also said: “I didn’t see a team I can be critical of in terms of work-rate and endeavour. It was a team fully committed, but we were just on the end of a tough result today.
“The reality is the chances (of staying up) are slim. The games are running out, but we need to keep fighting between now and the end of the season.
“Our challenge is to keep going for the final six games. We have to keep learning, keep trying to improve and finish the season as positively as we can do.”