Private equity investors have long looked to four large emerging markets for big returns: Brazil, Russia, India, and China. But the BRICs today don't quite fit the fast-growth that Goldman Sachs strategist Jim O'Neill described in the 2001 paper that coined the widely used acronym.

With each BRIC economy in some sort of trouble, private equity firms are increasingly putting their investment dollars to work in other less-developed markets—especially Southeast Asia and Sub-Saharan Africa—in hopes of better returns.

Money invested in non-BRIC emerging markets increased 18 percent in 2013, reaching a five-year high of $11 billion and representing 44 percent of total capital invested in emerging markets, according to a recent study by the Emerging Markets Private Equity Association. At the same time, total capital invested in the BRICs declined 20 percent between 2012 and 2013 and was 38 percent lower than in 2011.

"Investors are certainly looking beyond the BRICs, acknowledging that consumer driven growth is accelerating most in these new markets," said Aly Jeddy, partner at The Abraaj Group, a global private equity firm that runs $7.5 billion across more than 20 sector and country-specific funds. "Investors are increasingly as wary of BRICs hype as they are weary of the unattractive returns many of the funds in these markets have delivered."

To be sure, the BRICs are still a force. China, India and Brazil alone still accounted for more than 50 percent of total capital invested in emerging markets and more than 30 percent of all funds raised, according to the same EMPEA report. But the recent pullback in all funds raised from investors for emerging markets—from $45 billion in 2012 to $36 billion in 2013—was largely a result of fewer funds raised targeting China, India and Brazil.

No region has gotten more money outside the BRICs than Southeast Asia.

In 2013, fund managers invested a five-year high of $2.2 billion and raised $2.9 billion for the region, a six-year high. In 2011, so-called emerging Asia countries like Indonesia, Malaysia, the Philippines, Thailand and Vietnam received just 7 percent of emerging market private equity investment. That increased to 17 percent in 2012, and 23 percent in 2013.