Barnack were knocked out of the John Wilcox Cup at the semi-final stage, losing by five wickets at Peterborough on Sunday.
Barnack chose to bat first in a tie that doubled as a Rutland League Division One match but were undone by a good batting and fielding display from the city side.
Marcus Howard reached 58 not out, Scott Howard took five catches and Ben Chance claimed 4 for 46 as Barnack slipped to 155 all out. Shahid Muhammed top-scored with 46 for Barnack.
Peterborough reached their target inside 40 overs and will face Uppingham Town in the final at the end of August.