Montella's side suffered back-to-back losses in Serie A thanks to Mounir Obbadi's late strike following a missed Alessandro Diamanti penalty.
It sees Fiorentina slip to sixth - a point off the final UEFA Europa League place - but Montella refused to criticise those who voiced their anger at the defeat.
"The team gave very little away to Verona, but we were too generous in trying to win it and we paid for that," the former Italy international explained.
"The players I selected were the ones that gave me most security, but maybe I was not good at encouraging the boys to the end.
"We lost three precious points and we are upset about this. The team deserved applause and boos, as is what happened.
"Whoever pays for a ticket has the right to whistle, the fans have always supported the team and we will play to the maximum to make up for this undeserved defeat."
A disappointing outing was made worse as the club confirmed Khouma El Babacar suffered a twisted knee, while Milan Badelj sustained a bruised nose.
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