The Florence outfit beat Udinese 2-0 on Tuesday to qualify for the Coppa Italia final and visit Denmark's Esbjerg in the UEFA Europa League round of 32 on Thursday.
And Montella feels the fixture congestion played its part as Fiorentina fell to a 2-1 home Serie A defeat to Inter on Saturday.
"I think Inter deserved to be in front in the first half, as they were quicker, more reactive and had the initiative," he told Sky Sport Italia.
"However, in the second half we played the better football and had been able to equalise, but unfortunately Inter got that goal.
"You can also add in the bad luck we had, as Mauro Icardi’s goal was offside.
"We were lacking in energy after the Coppa Italia game and ahead of the Europa League fixture. As Inter will acknowledge, playing in these tournaments takes something away from you in Serie A."
And Montella took real umbrage at Icardi's winning goal, claiming the officials made a basic error in allowing it to stand.
"It did seem something that was not exactly difficult to judge," he added. "It’s a mistake, not a complicated one to evaluate, but it can happen. We accept the error, just as we accepted worse than this.
"It’s a pity, as when these incidents happen they do affect the results and consequently the whole campaign."
Fiorentina sit fourth in Serie A, three points adrift of Napoli in the final UEFA Champions League qualification spot.
