Emerging market economists at Capital Economics forecast Russia will grow by no more than 2-3 percent per year over the next decade – well below the average growth of 7 percent seen during the country's "golden era" between 2000 and 2008.
"We suspect Russia will go from being one of the world's fastest growing economies to one of its biggest underperformers," said Neil Shearing and Liza Ermolenko in a research note from Capital Economics.
According to a flash government estimate in April, the Russian economy grew by 1.1 percent year-on-year in the first quarter of 2013, marking Russia's fifth consecutive quarter of slowing growth.
Shearing and Ermolenko forecast the BRIC nation will grow by just 2.3 percent for the full-year 2013, and 2.8 percent in 2014, and said one-off factors were responsible for its previous boom.
"On the supply side, rapid growth was made possible by two things. The first was the dismantling of the Soviet economy, which created huge amounts of spare capacity. And the second was the onset of market reforms, which spurred productivity improvements. Both of these factors allowed for increases in production, without the need for substantial investment," they wrote.
"On the demand side, a sharp increase in oil prices boosted Russia's income and hence spending power. We estimate that higher oil prices alone have increased Russia's export earnings by a cumulative $1.5 trillion or so, over the past 10 years."
Oil and gas account for a large and increasing share of Russian exports, making up around two-thirds of total exports in 2012. According to Fitch Ratings, Russia is the most oil-dependent of the world's 10 largest economies, with oil and gas accounting for 50 percent of federal government revenues and up to 20 percent of gross domestic product.
However, weak demand, particularly from China, and record U.S. stockpiles have weighed heavily on oil prices this year. Brent crude oil is down 14 percent from its 2013 peak of $119.17 per barrel; on Wednesday, Brent traded at $102.65.
(Read More: Oversupply to Keep Oil Prices in Check)
Nonetheless, Shearing and Ermolenko said Russian growth was more at risk from internal supply-side problems than a continued decline in oil prices.
"Russia's supply potential is more constrained. The productivity improvements that were created by initial market reforms have now been exhausted, while the spare capacity created during the post-Soviet transition has been used up.
"At the same time, demographic pressures mean the population is shrinking. In order to ease pressure on the supply side, investment needs to increase from its current low levels," they wrote.
Francesc Balcells, a fund manager in Pimco's emerging market team, agreed that increasing inward investment was vital, and said Russia must focus on accelerating structural reforms and improving its investment climate.
The country's weak environment for investment is reflected in the World Bank's 2013 "Doing Business" survey, which ranked it 117th out of 185 countries, below the likes of Brazil, Turkey, Poland and Chile.
Shearing and Ermolenko warned that without reforms to increase investment, Russia could enter a period of permanently weaker growth.
"Unlike in other emerging markets,Russia's low investment rate does not appear to stem from a low level of domestic savings. Instead a poor business environment and lack of investor protection seem to be the main obstacles. The government has recognized the need to raise investment, but we suspect that vested interests will frustrate change on the ground," they wrote.
(Read More: Russia in 'No Hurry' to Privatize: Deputy Minister)
Russia's former finance minister, Alexei Kudrin, flagged similar concerns last month when he took President Vladimir Putin to task on live television for blaming Russia's economic woes on the lackluster global economic climate.
"The main factors of this slowdown remain internal," Kudrin said during the televised session.
(Read More:Putin's Popularity Wanes as Russia's Boom Ends)
On Friday, the European Bank for Reconstruction and Development, which invests in former communist countries,warned that weaker activity in Russia was harming Eastern Europe as a whole. It sharply downgraded its 2013 growth outlook for the region to 2.2 percent, citing a slowdown in large regional players such as Poland and Turkey, and Russia in particular.
—By CNBC's Katy Barnato