The Cottagers are just outside the relegation places in the Premier League, two points ahead of Sunderland and Crystal Palace, who occupy bottom spot on goal difference.
Parker believes the defeat was harder to take as Fulham went into the game with just one defeat in four matches.
Fulham are back in action on Tuesday when they take on Norwich in the FA Cup in their third round replay.
The 33-year-old said: "It's not ideal. It's obviously a blow. I didn't really see it coming. Like you say we've picked up some good results.
"Obviously we went into today's game expecting to get the three points but it wasn't to be. And we go again.
"When you are down there, in the position we're in, often you find that. Inconsistency is the reason we are down there. And that's proven it again today.
"I never thought it was a 4-1 result. But we've lost the game. That's the most crucial thing. I thought in large we dictated and really dominated most of the game.
"But at the end of the day the results are key and Sunderland have obviously won 4-1, so it's disappointing.
"I think it's clear for everyone to see over the last few weeks we've picked up results. Today's a blip. We have to work out as a team what went wrong today and try and put it right.
"We're running out of games, so we need to try and put it right together and hopefully bounce back from this and go again.
"The season isn't long. We're at the other side of Christmas now and we're in a dogfight. It's going to be difficult for us and we've got to go out there with the mentality that we've got to try and win as many games as we can and give ourselves a chance.
"We're not giving ourselves a chance at times but, like I said, I think there were positives today.
"I think it is good we've got a game on Tuesday night which we can put right what we got wrong today hopefully."