Zian Flemming gave the Clarets the lead at Craven Cottage, before Fulham struck through Josh King, Harry Wilson and Raul Jimenez.
“It felt like an unjust final scoreline," said Parker afterwards. “We were really in the game for an hour.
“We imposed ourselves really well on the game and took the lead through a well worked goal. Once they scored one and then we gave them a second, the game went away from us.
“The goals they scored came at the wrong time for us and it really left us with a lot to do. The third was harsh on us but that’s the ruthlessness of this league, you get punished.”
He added, “I thought the general effort and commitment was there.
“This group crosses the line every week and represents the values we talk about on a daily basis. I can’t fault the lads for what they’ve given, but we just fell short again.
“There’s positives but we’ve lost the game so that’s hugely disappointing.”