Half a dozen of these upper caste leaders were aspiring for the post.
Rai, a new face of the party in Bihar, replaced Mangal Pandey, an upper caste leader.
The BJP's attempt to project Rai, belonging to the Yadav caste, is seen as an attempt to cut into the support base of Lalu Prasad's RJD and Chief Minister Nitish Kumar's Janata Dal-United.
Rai is the Lok Sabha member from Ujiyarpur and has been elected to the Bihar assembly four times from Jahipur.
The upper caste BJP leaders feel Rai's elevation won't help the Bharatiya Janata Party.
"This won't help us because the two top leaders of the state's ruling alliance are from OBC.
"The party should have appointed an upper caste leader in place of Rai," a senior BJP leader said on condition of anonymity.
An upper caste BJP legislator said Rai's appointment was bound to upset upper castes in Bihar.
Both BJP leaders told IANS that the upper castes, BJP's traditional supporters for over two-and-a-half decades in Bihar, would feel let down as the party was now dominated by OBCs.
"The Leader of Opposition in the Bihar assembly, Prem Kumar, is also an OBC. Now Rai has replaced Pandey also," one of them pointed out.
According to them, upper caste BJP leaders may not express their unhappiness over Rai's appointment in public now but it would surface sooner or later.
Upper caste BJP leaders belonging to the landed Bhumihar and Rajput communities had targeted former Deputy Chief Minister Sushil Modi time and again for his style of functioning.
In Bihar's caste-ridden politics, it is widely believed that the BJP is divided into caste lines.
Due to this, Amit Shah did not name a Chief Ministerial candidate during the 2015 assembly polls to avoid angering any social group.
In Bihar, most other political parties also lean on backward castes, Dalits and Muslims.