Veteran goalkeeper Mark Schwarzer captained the side which included a mix of first-team players and reserves at FC Grimma's Stadion der Freundschaft.
There were few chances during the first half, with Marcello Trotta's volley well saved by the Koge goalkeeper.
Following the restart, Fulham manager Martin Jol changed his entire XI, which saw new signings Sascha Riether and Mladen Petric make their bow.
However, despite more pressure, the Cottagers continued to be frustrated.
Celtic failed to score for a second pre-season game as they fell to a 1-0 defeat against German third division side Stuttgart Kickers.
Neil Lennon's experimental first-half line-up conceded a headed goal just before the break and they struggled to carve out any second-half openings.
Their hosts had several chances to add to the lead in the final 20 minutes.
Celtic opened their tour with a goalless draw against Augsburg in midweek.