Sam Allardyce had Popov on trial last month but Williams revealed that the club pulled out of the deal because no bid came in for out-of-favour Rovers striker Roberts.
Williams told the Lancashire Telegraph: "We were expecting a bid for Jason Roberts. We were confident he would be fit and ready to fight for his place if he was still with us, but deep down I think we wanted a move. The problem was we couldn't let him go without a replacement.
"Four strikers are needed. We covered our position with Ivelin Popov ready to come to Rovers. His club knew the deal was dependent on Jason leaving but in the end no bid came."
He added: "Five strikers was never going to be an option, nor was letting Jason leave on a free."
With a move to Rovers off, Litex Lovech forward Popov instead joined Turkish outfit Gaziantepspor for a reported fee of £1.2million before playing for Bulgaria in their 4-0 defeat to England at Wembley on Friday night in a Euro 2012 qualifier.