Next up is a trip to Parker's former club West Ham - a match in which the former England international, named Fulham captain for the first time this weekend, knows he and his team-mates need to stop the rot.
"We were always in the game and when we got it back to 1-1 I felt we could push on for the win or at least get a draw," Parker, whose fortuitous goal brought Fulham level, said.
"It wasn't meant to be so we ended up coming away with no points which is disappointing.
"When you look at the table it does not look pretty. It is for all to see.
"We need to get some points and get them quickly or it is going to be a tough season for us. I think we know that.
"The key is getting some results. If we can win a couple of games all of a sudden the pressure can come off and things happen for you a bit.
"There's only so many times you can say you played well without getting the points. We hit the post and had a few chances but we didn't the win the game."
Darren Bent's strike off the post came in a first half that Fulham dominated, although the positivity around Craven Cottage soon disappeared as Swansea grew into the game.
Supporters made their feelings known to Jol and his players during the 2-1 defeat - Fulham's eighth loss of their 12 Premier League fixtures.
"I can understand why they are frustrated," Parker said. "All of us are and I can see where the fans are coming from.
"We are bitterly disappointed along with the fans. They pay their money and want to see us winning games and we are not doing that."
The loss to Swansea, for whom an Aaron Hughes own goal and Jonjo Shelvey strike proved decisive, was hardly the response Fulham had hoped for after Rene Meulensteen's much-publicised appointment as head coach.
The highly-rated Dutchman was a key member of the Manchester United backroom staff under Sir Alex Ferguson and his appointment represented quite a coup for the west Londoners.
"We have only worked for three or four days," Parker added. "It is a new person in the building.
"I know it is a cliche, but at this part of the season where we are, we have to stick together.
"Hopefully Rene can bring a bit of experience, guidance and something different to help us get some points."
Meulensteen is seen by many as Fulham's manager in waiting and has had previous experience as top man in Qatar, Denmark and, briefly, Russia.
In Denmark he joined Brondby as successor to Michael Laudrup, who was pleased Swansea were able to start an important period of the season with a morale-boosting win.
"We have another competition Thursday against Valencia, and the Sunday we play one of the favourites for the title, Manchester City," the Dane said after overseeing his first win in over a month.
"But I do know there is one thing in football that gives confidence - wins. This is the first game of 12 in six weeks so it's so important."
- Sports & Recreation
- Martin Jol