The Cottagers had only won one of their four summer games before taking on Malaga at their Estado Rosaleda base in the Trofeo Costa del Sol.
Goals from Alex Iwobi and Ryan Sessegnon had Fulham 2-1 up going into the closing stages, before Eneko Jauregi scored a late equaliser from the penalty spot, after a controversial handball decision against Calvin Bassey.
New Fulham boss Alvaro Arbeloa was enraged by the call and the former Spain international was subsequently sent off for his protests.
The Fulham players then refused to take part in a penalty shootout to settle the game - a common feature of some preseason tournaments - where a trophy is there to be won.
Rumours of Fulham declining the shootout ranged from their support of Arbeloa, but also an indication they were not informed of possible penalties before the game, and their involvement could have seen the squad miss their flight home.
Malaga eventually rolled a penalty into an empty to win the competition via forfeit - as a furious Fulham statement claimed an agreement had not been fulfilled - which Malaga claimed was untrue.
Fulham now wrap up their preseason at home to VfB Stuttgart on August 15th before a Premier League campaign opener at home to Chelsea nine days later.