A first half goal from Antoni Sarcevic proved to be the difference between the two sides during a below-par first half from the visitors.
Stags did have a good chance to level with Michael Smith missing an excellent chance close to half-time.
Harry Lewis was the stand-out performer with a number of good saves to keep Stags in the game.
Here is how we rated the performances today (First 80 mins only). Give us your ratings verdict and thoughts on the result via our social media channels.
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5. Louis Reed 6
Battled hard to give Stags a foothold in the game but found the going tough against an energetic Bradford midfield and didn't have his usual influence. Photo: UGC
6. George Maris - 6
Put in a good shift as he continues his comeback from injury. Anchored the midfield well Thompson in the closing stages as Stags pushed for an equaliser. Photo: Getty Images
7. Nathan Moriah-Welsh - 5
Had a decent beginning during a fast start by Stags but faded badly as the game went on. Looked lost and failed to influence the game before being subbed at half-time. Perpahs should have done better to win a header in the build-up to Bradford's opener. Photo: UGC
8. Liam Thompson - 5
Not one of his better games for Stags. Worked tirelessly as ever but needed to take more care of the ball and help Reed shore up midfield more. Photo: Chris & Jeanette Holloway