'Gers were beaten to the punch for the Maccabi Haifa star by Spanish club Real Mallorca, who offered more for his services, and Whyte insists he will not be pressured into paying big transfer fees to strengthen the Scottish Premiership-winning squad.
"(Manager) Ally (McCoist) has targets in mind and we are actively negotiating to bring in several new players," Whyte told the Scottish Daily Mail.
"The fact Hemed has gone elsewhere is disappointing but we will not overpay for players. He was not our first choice anyway.
"But they would have been forced to sell the best players and substantially reduce the wage bill."