Lavrov's comments came at the annual Munich Security Conference, RIA Novosti reported.
"Why are there no voices condemning those who seize government buildings, attack the police and adopt racist and anti-Semitic slogans? Why do European leaders actually encourage such actions, when they would quickly move to punish them at home?" Lavrov said.
"What would be the reaction from the European Union, if members of the Russian government began to openly express support, including personal visits, to rioters in London, Paris or Hamburg?" he added.
European Union High Representative for Foreign Affairs and Security Policy Catherine Ashton Friday called attempts to arrest Ukrainian activist Dmytro Bulatov from his hospital bed "unacceptable," Interfax reported.
"We had an in-depth discussion about the situation in Ukraine. I am deeply alarmed by the violence and cases of intimidation and torture. I am particularly appalled by the cruel treatment and torture of Dmytro Bulatov and reports that there are attempts to arrest him from his hospital bed. This is completely unacceptable and must stop immediately," Ashton said in a statement. "The situation in Ukraine is deeply worrying and I will be returning to Kiev next week, on behalf of the European Union."
Medical workers at the hospital where Bulatov is being treated have blocked police from questioning the activist, the BBC reported.
Bulatov was discovered badly injured on the outskirts of Kiev Thursday. The activist said he was kidnapped and tortured.
He didn't know who kidnapped him, but said they spoke with Russian accents.
"They crucified me, so there are holes in my hands now," Bulatov said. "They cut off my ear, cut up my face. My whole body is a mess. You can see everything. I am alive. Thank God for this."
Amnesty International called Bulatov's ordeal a "barbaric act which must be investigated immediately".