On 24 November 2013, Kone scored his first goal of the 2013–14 season in a 1–1 home draw against Internazionale, finding the net in the 12th minute. In the penultimate matchday on 11 May 2014, Bologna, after a 1–2 home loss to Catania, were relegated to Serie B. After the defeat, 300 Bologna fans surrounded the squad and prevented them from reaching manager Davide Ballardini, instead screaming for contracts to be torn up over a cordon of riot police. Captain Kone—as one of a few players to emerge from the season with any value at all—was consoled by a supporter after breaking down in tears in the melee. "The dressing room is destroyed, we are mortified. Kone has been crying alone on the pitch," coach Ballardini was quoted as saying in "La Gazzetta dello Sport".