Arsenal confirmed on Tuesday that Mkhitaryan will not be playing in the final against Chelsea due to fears over his and the club’s security.
There are no diplomatic relations between Armenia and Azerbaijan because of a longstanding conflict over the disputed Nagorno-Karabakh region.
Koscielny, the Arsenal captain, told BBC Radio 5 Live that countries with such conflicts should not be able to host European finals.
“I am not very happy,” Koscielny said. “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.”
Mkhitaryan spoke on Tuesday of his “hurt” at missing the match, which will determine whether Arsenal achieve their primary objective of qualifying for next season’s Champions League.
“We had to take the tough decision for me not to travel with the squad to the Europa League final,” he said. “It’s the kind of game that does not come along very often and I admit, it hurts a lot to miss it.”
Vinai Venkatesham, Arsenal’s managing director, said the situation was “completely unacceptable” and “extraordinarily sad”.
“It is not our decision or Henrikh’s but one we made together,” Venkatesham told the FT Business of Football summit. “We don’t feel he can travel to a major European final and that’s extraordinarily sad. He has had that opportunity taken away from him, one that is a rare opportunity for any player.
“We’re losing the opportunity of having him to help us win a major trophy. It’s an extraordinary shame. All we can really do is make our point very clearly to Uefa. After the final we will explain to them why it’s unacceptable and must avoid it happening to Arsenal or any other club ever again.”