Yadav said his party MPs did not allow the bill to be passed by Lok Sabha on the last day of the Winter session of Parliament which ended yesterday.
He said his party has only eight members in Rajya Sabha where the Constitution (117th Amendment) Bill, 2012, was adopted.
"Our party may have only eight members in Rajya Sabha, but is strongly opposed to the issue and did not allow the bill to get passed in Lok Sabha by opposing it alone," he said.
The SP supremo said his party may not have adequate numbers in Parliament, but people outside were with it.
SP is opposed to reservation in promotion, a demand put forward by Mayawati, whose BSP had apparently extended support to the UPA on the FDI issue as a quid pro quo for passage of the quota bill.