Inter opted to dismiss former boss Walter Mazzarri last month after Inter won just four of their opening 11 league matches.
The Milan side acted swiftly to draft in Mancini, who won three straight Serie A titles in his first stint at San Siro before being sacked in 2008.
Since resuming the role Mancini has overseen a 1-1 derby draw with Milan and a spirited 4-2 defeat at Roma, either side of a 2-1 UEFA Europa League victory over Dnipro - a game in which Kuzmanovic was on the scoresheet.
And the midfielder believes Inter are playing with less pressure since Mancini was re-appointed.
"The atmosphere has improved, no doubt," he told Gazzetta dello Sport.
"There is not the same tension that there was a few weeks ago."
The Serbian also hopes Inter can win back the affection of the fans after several incidences of supporter dissatisfaction at home matches this season.
"I understand the feelings of the fans," he added. "I understand the boos when things were not going well.
"But now we need their contribution so when we play at San Siro we feel at home and not as if we were playing away."
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