Wolverhampton grabbed a late winner thanks to Adama Traore’s strike which beat Alphonse Areola at the near post to condemn Fulham to their fourth straight loss.
“It’s a tough one to take,” Parker said. “It’s not going to be a tough one to bounce back from.
“It’s a painful one tonight and you obviously see that in the scenes at the end of the game, in terms of this team, how desperate this team are to be successful.
“I asked the team to show fight, to show desire, to leave everything on that pitch tonight, and to a man - and I include the boys who were on the side - we did that. That’s the cruel side of football sometimes.”
The Cottagers have now played 32 matches with 26 points, three behind 17th-placed Newcastle who have played two games less.
Burnley and Brighton are both not safe either in 15th and 16th with 33 and 32 points respectively.
“We’ve put ourselves in this position, with a real fighting chance, because of what you’ve seen at the end of the game, a team and a group of players that are desperate, that care passionately about us being successful this year, and with that spirit and with that desire, you’ve always got a chance,” Parker said.
“You’ve always got a chance. And that will be our mantra, and we will continue. Its painful, were hurt, disappointed tonight, but as always when this happens, you get your guard up and you come out swinging. And thats what well do.”