The foreign minister made the comments at a news conference in Moscow on Wednesday with Ali Babacan, his Turkish counterpart.
Lavrov said: "To put it mildly, it is a bitter irony that this mission to ensure the supremacy of the law in Kosovo is being sent in breach of the highest international law."
Russia, a close Serbian ally, has been flexing its growing clout on the world stage but proved powerless to prevent Kosovo from announcing its split from Belgrade on Sunday.
The state was promptly recognised by most of Europe's largest nations and the United States, a move Russia says will open a "Pandora's Box" of separatist tension across Europe.
Nato-led peacekeepers in Kosovo have already sealed off two border crossings with Serbia for 24 hours after they were torched by angry Serbs.
The EU is expected to deploy the 2,000-strong mission by June.
It will oversee training and institution-building, with limited rights to intervene to fight organised crime and corruption or hunt war criminals.
Vladimir Putin, Russia's president, said last week that the West was guilty of double standards in pushing for Kosovo's independence, a charge Lavrov repeated.
The leader of Russia's Orthodox Church said on Wednesday that Kosovo's independence would sow disorder and could lead to separatist tension across the world.
Patriarch Alexiy II said: "It is an... event which has unilaterally upset the balance in the world and could lead to very tragic events in a whole host of areas across the globe where separatist sentiments are warming up."
The United States and most European Union countries say Serbia relinquished the moral right to rule the people of Kosovo because of brutality under Slobodan Milosevic, the late Serbian president.
However, Serbs have vowed never to surrender Kosovo, which is dotted with Orthodox monasteries and is considered the spiritual homeland of Serbia.
Kosovo has been under United Nations supervision since 1999, when Nato bombing forced a withdrawal of Serb forces that had been attacking the province's ethnic Albanian majority.