Dmitry Medvedev, Russia's president, said new legal mechanisms needed to be created to prevent a recurrence.
"The recent gas crisis has shown that things are not all right here," Medvedev said.
Barroso called for "positive interdependence" in relations.
"It is important now to create conditions for this kind of crisis not to happen again. We believe energy security is a very important sphere of interest for Russia and the European Union," he said.
"And this positive interdependence is more important now than ever because we are facing a very serious global financial crisis."
War with Georgia
Ties between the 27-nation bloc and Russia were already strained over last year's war with Georgia.
Russia says the war was provoked by Georgian aggression and recognised the two separatist regions, Abkhazia and South Ossetia, as independent states.
The EU brokered a ceasefire between the two sides but waited impatiently for Moscow to withdraw its troops from inside Georgia.
The EU, Russia's biggest trading partner, has been unsuccessful in the past at bringing Russia into closer ties with it.
Diplomats say they do not expect any major breakthroughs at the talks over issues such as trade, energy, and the Kremlin's plan to build military bases in two breakaway regions of Georgia.