Fulham eked out a goalless draw in their third qualifying round first-leg match at RNK Split in Croatia.
Fulham were unable to force a clear opening in the first half, while RNK's Ante Erceg came closest to scoring, shooting wide when through on goal.
The Premier League side had chances early in the second half but thereafter the hosts looked more likely to secure a winner.
The second leg takes place at Craven Cottage next Thursday.
Fulham manager Martin Jol named a strong starting line-up, with veteran midfielder Danny Murphy skippering the side at Dugopolje's Stadion Hrvatski Vitezovi and Andrew Johnson and Bobby Zamora given a chance to hone their strike partnership.
New signings Pajtim Kasami, Csaba Somogyi and Marcel Gecov were named among the Cottagers' substitutes.
But a blocked Damien Duff shot was the visitors' only moment of note in the opening 25 minutes and Fulham were continually exposed down the flanks.
They began the second period more positively and came close to scoring five minutes after the restart when Johnson broke down the right and cut the ball back for Matthew Briggs, but his shot into an empty goal was thwarted by a lunging challenge in the six-yard box.
John Arne Riise came close to finding the bottom corner with a low drive three minutes later as the visitors began to take more control of the game, before Zamora blazed a long-range effort wide.
RNK, though, were still proving dangerous and an ambitious 30-yard effort from Ante Vitaic looked dangerous before a deflection.
Split began to press as the game entered the latter stages and Mark Schwarzer was forced to save when substitute Duje Cop managed to turn his marker and force a shot in the 18-yard box.
Jol brought on Steve Sidwell for Dickson Etuhu in a bid to change the game but the only impact the former Aston Villa midfielder had was receiving a yellow card a minute after coming on.
The Fulham boss made another switch with 10 minutes remaining, handing recent signing Kasami his debut in place of the ineffective Zamora.
However, the former Palermo midfielder's introduction failed to gee up his new team-mates and Cop twice came close to scoring in the final 10 minutes.
First he darted a header across the face of the goal, then he turned Chris Baird but could only manage a feeble shot that Schwarzer easily stopped.