Callum Cooke grabbed a late reply for Bradford who have now not won in their last five league games.
City, without six injured senior players, conceded a free-kick early on when Ferry was brought down by Oscar Threlkeld and recalled defender Ludwig Francillette put the ball wide after Jack Powell’s goal attempt was blocked.
Bantams leading scorer Andy Cook blazed over from 14 yards before directing a header over from a free-kick by Callum Cooke.
Midfielder Ferry, on loan from Southampton, struck to put Crawley ahead six minutes before the break by stabbing in a free-kick from Jake Hessenthaler for his first goal in senior football.
Reds keeper Glenn Morris preserved the advantage by parrying a header by Yann Songo’o before Francillette headed against the post at the other end.
City looked more purposeful after the interval and Threlkeld was inches away from converting a Gareth Evans cross.
City boss Derek Adams sent on substitutes Levi Sutton and Kian Scales but Tsaroulla doubled the lead on 73 minutes with a low shot from just inside the area.
Cooke reduced the deficit eight minutes from time by firing in at the far post but City could not produce an equaliser.