Goals from Burnley duo Lukas Jutkiewicz and Matthew Taylor earned the Clarets the win although Parkinson's side did have a number of promising opportunities to score during the contest.
The match was City's final scheduled pre-season friendly of the summer before their season opener at Swindon Town next weekend.
Bantams PlayerHD subscribers can watch Phil Parkinson's FULL post-match Burnley assessment, including his thoughts on Stephen Darby's return to action and the signing of Paul Anderson, right now by clicking HERE.