Montella feels Fiorentina are "invaded by enthusiasm" from the fans after they consolidated fourth place by beating Milan.
"I am satisfied, as this was a great day for us and the supporters considering the way it developed and the responses given by the team," he said of their 3-1 result at San Siro.
It was a particularly impressive victory considering star striker Stevan Jovetic was out injured.
"These are three deserved points, even if we were a little lucky in the final minutes. I really liked the way we played, because the team showed it understood each moment of the match.
"We might've been a little less spectacular and a little more clinical compared to the start of the season, but still could have finished it off earlier."