Josh Laurent had earlier got the home side up and running with a well-taken goal, but Burnley wasted some golden chances to put the tie out of sight.
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Rhys Oates got them back on level terms and the game appeared to be heading towards extra-time, but Reed stepped up and delivered a peach of a free-kick beyond Max Weiss.
It sparked more boos at the full-time whistle, as the Clarets squandered the opportunity to build on Wednesday night’s win at Crystal Palace.
Here’s how Burnley’s players rated:
Burnley found themselves on the wrong end of another cup shock. Photo: Kelvin Lister-Stuttard
1. Dismal
Burnley found themselves on the wrong end of another cup shock. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
Well beaten by Mansfield’s stunning free kick and not much he could do about the equaliser either. Otherwise didn’t have to do much. (Photo by George Wood/Getty Images)
2. Max Weiss - 6/10
Well beaten by Mansfield’s stunning free kick and not much he could do about the equaliser either. Otherwise didn’t have to do much. (Photo by George Wood/Getty Images) Photo: George Wood
Showed plenty of composure for his goal, which he took really well. Filled in well out of position at right-back too. Photo: Kelvin Lister-Stuttard
3. Josh Laurent - 7/10
Showed plenty of composure for his goal, which he took really well. Filled in well out of position at right-back too. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
Fortunate to get away with his untimely slip at the start of the second half and looked shaky defensively. Photo: Kelvin Lister-Stuttard
4. Hjalmar Ekdal - 5/10
Fortunate to get away with his untimely slip at the start of the second half and looked shaky defensively. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard