The home defeat hardly represented Liverpool's best possible preparation for Saturday's FA Cup Final date with Chelsea.
In a meeting between two of new England manager Roy Hodgson's most recent employers, Liverpool's wretched home league form continued as they failed to record a victory for the 13th time in 18 games.
More alarmingly, Liverpool could also end the season outside the top eight in the top division of English football for the first time since 1954.
Manager Kenny Dalglish elected to leave four potential Wembley starters out of his line-up - goalkeeper Pepe Reina, plus Steven Gerrard, Daniel Agger and Luis Suarez - and his decision looked a costly one when Fulham took the lead after only five minutes.
From the game's first attack, Clint Dempsey's pass sent former Liverpool full-back John Arne Riise down the left-hand touchline and his cross into the six-yard box was met by another former Anfield player Alex Kacaniklic.
The 20-year-old's mishit shot bounced against Skrtel's legs, wrong-footing Doni on its way into the net.
Liverpool responded in reasonably impressive fashion, Skrtel quickly trying to make amends as he headed wide from a Fabio Aurelio free-kick, although Fulham might have doubled their lead on 15 minutes when Dempsey threaded through for Pavel Pogrebnyak whose first-time shot was well parried by Doni.
Maxi Rodriguez collected Dirk Kuyt's lay-off and sent a shot soaring over the Fulham bar although Andy Carroll was becoming the most impressive attacking presence in a red shirt.
After 23 minutes, Kuyt latched onto a loose ball after Carroll's progress was blocked and volleyed inches wide.
Before the half-hour, Mark Schwarzer mis-handled a cross under pressure from Carroll, allowing Maxi to square the ball for Jonjo Shelvey whose shot beat the Fulham keeper but not defender Brede Hangeland who cleared off the line.
Dalglish brought on Stewart Downing and switched to a 4-4-2 formation at the interval with early second half signs looking promising as Shelvey volleyed over and Jay Spearing dispossessed Dempsey before testing Schwarzer with a 20-yard shot which the goalkeeper kept out at full-stretch.
Hangeland was also required to make an impressive and timely tackle to halt the progress of Maxi as he surged into the area and bore down on Schwarzer's goal.
But Fulham began to exploit some of the gaps created by Liverpool's increasing attacking urgency.
Dempsey headed just wide from Damien Duff's 53rd minute corner, substitute Kerim Frei created room for himself on the edge of the area and saw his well-hit shot impressively touched onto the post by Doni.