Armenia and Azerbaijan are engaged in a conflict over the disputed Nagorno-Karabakh region, which has sparked fears over Mkhitaryan and Arsenal's safety in the Azerbaijan capital of Baku.
UEFA have been criticised for their decision to host a major final where such safety concerns exist, though Europe's governing body insisted that they had received assurances over Mkhitaryan’s safety.
Koscielny, however, feels those assurances were not enough and called on UEFA to not hold any future finals in countries with such political problems.
“I am not very happy,” Koscielny told BBC Radio 5 Live. “First because we need to leave one player here, because he can’t play in the final.
“I think UEFA needs to know about the different problems they can have with the politics in the country. When one country has a problem with another they should not give the final to that country.
“For us it is difficult because we want to have Micki with us. He is an important player for us.”
Arsenal manager Unai Emery, a three-time Europa League winner with Sevilla, indicated the decision was made by Mkhitaryan and not the club, but he understands the midfielder's reasoning.
"It's bad news. We need to understand the political problem, but we must respect it," Emery told a news conference on Tuesday.
"I spoke with Mkhitaryan this morning but it's a very personal issue. He wants to play with the team. He spoke to his family.
"I come from the Basque country and we have a big political problem, too. I can understand his decision.
"It is very personal also. The decision is not in my hands, but I respect him."
The Baku Olympic Stadium will play host to the final on May 29.