His comments came ahead of possible sanctions by the Confederation of African Football against his national team after Senegal's players walked off the pitch in protest at a VAR-awarded penalty before returning to beat hosts Morocco 1-0 after extra time.
A group of Senegalese fans clashed with Moroccan security as they tried to enter the pitch in protest following the penalty decision.
Eighteen Senegalese supporters have been arrested and will stand trial in Morocco over the incidents.
Social media users from the two countries have traded accusations since the final.
Speaking at the opening of a Moroccan‑Senegalese joint commission in Rabat, one week after the final, Sonko said his visit comes in a context "charged with sporting emotion, deplorable misconduct and images that have at times been painful for two peoples deeply bound to one another."
"The misbehaviour observed here, and there should neither be denied nor dramatised," he said.
The incidents "should be understood as emotional excesses fuelled by passion, rather than as political or cultural rifts," he added.
The remarks marked the first time a senior Senegalese official has acknowledged the African Cup final incidents in those terms, ahead of possible disciplinary measures by CAF.
The Moroccan football federation said it was pursuing legal action with CAF and FIFA following the final incidents.
CAF said it would take "appropriate action" after reviewing the match incidents, while FIFA President Gianni Infantino condemned the behaviour of Senegal's players and members of the coaching staff.
President Bassirou Diomaye Faye congratulated the Senegalese team in Dakar and thanked Morocco for its organisation of the tournament.
Senegal is among Morocco's closest allies on the continent. Dakar backs Morocco's sovereignty over the disputed territory of Western Sahara, where it operates a consulate.
Moroccan Prime Minister Aziz Akhannouch said at the same event that centuries‑old ties with Senegal were strong, but he did not congratulate Senegal on its African Cup win.
Morocco's king had said the tournament was a success for Africa and that the "regrettable incidents" that marred the final would not undermine African fraternity.