In the summer, the Galiarossi hierarchy were searching for a replacement to Luis Enrique, who stepped down from his position after just one season in charge.
Former player Montella, who had previously worked as a caretaker manager when Claudio Ranieri was sacked in February 2011, was available after leaving Catania by mutual consent.
The 38-year-old had led Rossoblu to a mid-table finish in Serie A and had been heavily linked with a return to the Stadio Olimpico.
However, Roma instead hired Zeman, while Montella was snapped up by Fiorentina.
"Montella? No, of course we don't feel regret," Sabatini told Sky Sport Italia.
"Montella is doing great things at Fiorentina and we are pleased for him, but Zeman is our coach and we will all work together to do better as time goes on."
Roma lie seventh in Serie A, with Fiorentina a place above them in sixth.