Neither Farnborough or Barnet could break the deadlock at Cherrywood Road.
Barnet had the lion's share of possession in the first half and Dean Sinclair's fierce drive forced a fine save out of goalkeeper Craig Holloway.
At half time, Farnborough's fans staged a sit-down protest on the pitch over a proposed takeover of the club.
Farnborough midfielder Gary Holloway nearly snatched a late winner with a fine strike from the left channel which just missed the target.
Farnborough: Craig Holloway, Rooney, Theo, Charles, Townsend, Mulhern (Allen-Page 62), Hughes, Gary Holloway, Taggart, Blackman, Chaaban (Harkness 83). Subs Not Used: Osborn, Miles, Belaid.
Booked: Theo, Mulhern, Chaaban, Townsend, Charles.
Barnet: Gore, Hendon, Plummer, King, Clist, Strevens, Lee (Bailey 79), Sinclair, Graham, Grazioli, Hatch (Roache 74). Subs Not Used: Millard, Lopez, Gwyther.
Ref: S Beck (England).