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Arsene Wenger's side were attempting to overhaul third placed Manchester City in the race to qualify automatically for the Champions League group stages.
City's 2-0 victory at Bolton meant Arsenal's efforts were always going to be academic, but the Gunners were unable to finish a frustrating season on a high note.
Arsenal's season has tailed off dramatically since the League Cup final defeat to Birmingham and they now face a potentially tough qualifier at the start of next season to reach the Champions League group stages.
They twice fell behind at Craven Cottage, first to Steve Sidwell's 26th minute opener and then Bobby Zamora's 57th minute header.
Robin van Persie struck the first equaliser before Fulham's Zoltan Gera was sent off for a two-footed tackle on Thomas Vermaelen.
Theo Walcott hit Arsenal's 89th minute leveller but Fulham finished in eighth spot and could qualify for the Europa League through the Fair Play table.
Wenger had conceded beforehand some of his players were running on empty after a draining campaign that ultimately left the club empty-handed for a sixth successive season.
The closing weeks of the season have been far kinder to Fulham manager Mark Hughes, who oversaw a transformation in his side's fortunes since the turn of the year.
The prospect of matching the club's best ever finish was clearly a powerful incentive for the home side who certainly didn’t approach the game with one eye already on the beach.
Chances were few during the opening 25 minutes however, with Arsenal left back Kieran Gibbs producing the only notable effort with a powerful downward header that forced a sharp reaction save from Mark Schwarzer.
Fulham had been less incisive in their attacking moves but broke the deadlock in the 26th minute when Zamora broke free on the right and pulled the ball back for Sidwell, who struck his second goal in three games from close range.
Arsenal responded immediately thanks to a move crafted by Abou Diaby who burst from midfield, exchanged passes with Marouane Chamakh before picking out Van Persie.
The Holland striker broke into the Fulham area and finished left footed to level.
The game opened up after the break with Fulham forwards Zamora and Andy Johnson unsettling the visitors defence.
It was the home side, though, who found their way ahead, taking the lead for a second time through Zamora.
Clint Dempsey found Jonathan Greening on the left hand flank and the midfielder rounded Arsenal right back Bacary Sagna before crossing towards the near post where Zamora headed home for his seventh goal of an injury-affected season.
Wenger responded by making a triple substitution in the 64th minute, introducing Walcott, Andrey Arshavin and Emmanuel Eboue.
They finally worked their way back level with a fine solo effort from Walcott in the 89th minute as the England winger cut in from the right flank and drilled home a fine low strike.
