The Viola lost for the first time in nine games at the weekend when they fell to a 1-0 defeat against Cagliari, and Montella is keen for his players to bounce back with a victory in their cup clash.
"Udinese are a good, strong, young team," he told reporters. "They adapt well to their opponents, they are not defensive and they will be a dangerous opponent for us.
"We accept the criticism for the Cagliari match, even though it is exaggerated. I alone take the blame and responsibility.
"The team tried their best, the only things missing were tactical elements and it's my fault."
Fiorentina are currently fourth in the Serie A table.