Swindon failed to break down 10-man Bradford City.
The Bantams had defender Andrew Davies sent off for foul and abusive language following an off-the-ball incident with Swindon's Jake Jervis.
Town's best chance to win the game came when Cristian Montano's shot in the last minute whistled past the post.
Defeat would have been harsh on the visitors who defended astutely throughout and for whom keeper Matt Duke was a relative spectator.
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Swindon manager Paolo di Canio told BBC Wiltshire:
"When everything goes wrong, a game like this makes you even more frustrated.
"I can't blame my players because they gave everything. Tactically not in a good way obviously.
"But I can't say anything about the commitment and already I have said something to them but we will analyse the situation on Monday."