Speaking to senior officials at a meeting broadcast on state television, Putin said those companies had suffered major losses as a result of exiting a large and lucrative market.
"Today many of them (Western brands), under pressure from their governments, are leaving our market. All the best to them," he said, briefly waving his hand in a farewell gesture.
"Nothing (in Russia) has collapsed and nothing is falling apart. Our companies and entrepreneurs are picking up these enterprises, and even entire sectors, and continue this work very successfully," Putin added.
Scores of Western companies - from energy producers to food and clothing chains - have left Russia in the last year, amid unprecedented sanctions imposed by Western countries after Russia deployed tens of thousands of troops to Ukraine.
Some departed firms have sold their assets to local investors for nominal fees.
Western sanctions over the conflict have upended some sectors of Russia's economy, cutting its biggest banks from the SWIFT financial network, curbing its access to technology and restricting its ability to export oil.
While the government and central bank have acknowledged "difficulties", Moscow says its economy is resilient and that sanctions have boomeranged against the West by driving up inflation and energy prices.
Putin also said on Thursday that Russia should build a system for developing drones and aim to become a "source of technology and competence".
Russian forces have made extensive use of drones, including those purchased from Iran, during their ongoing military campaign in Ukraine.
(Reporting by Felix Light; Editing by Gareth Jones)