Leicestershire County Council applied for the funding to improve services and secure the future of subsidised routes serving rural areas.
However, the Department of Transport (DfT) said areas "not showing sufficient ambition would not be funded".
Thirty-one counties, city regions and unitary authorities have been chosen for funding to level up their local bus services in the latest awards from the bus transformation programme.
Mr O'Shea, cabinet lead for highways and transport, said "We're really disappointed that Leicestershire has again been overlooked in a bid for government transport funding… We're not taking this lying down and have already raised this with local MPs and asked the Department of Transport to explain why our bid was turned down. Once we get that feedback, we'll consider our next move."
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