Pressley, who last month revealed dressing-room “unrest” at Tynecastle, was a shock omission from the Jambos squad while Scotland team-mates Paul Hartley and Robbie Neilson remained on the bench.
Hearts started strongly but Andrius Velicka fired them ahead against the run of play midway through the second half before Russell Latapy levelled with six minutes left.
FALKIRK: Lambers, Ross (Dodd 17), Scobbie (Twaddle 63), Barr, Milne, Latapy, Cregg, Thomson, O’Donnell (Craig 63), Gow, Stokes.
HEARTS: Gordon, Zaliukas, Wallace, Karipidis, Berra, Barasa, Brellier (Hartley 90), Aguiar, Mikoliunas, Velicka, Mole (Makela 75).
Referee: M McCurry (Scotland).
The FA Cup sponsored by E.ON: First round: Havant and W 1 Millwall 2; Macclesfield 0 Walsall 0.
Bank of Scotland Scottish Premier League:Falkirk 1 Hearts 1.
Eircom League Premier Division: Waterford 0 Derry City 1.