Central banks have long used inflation expectations to set policy, including interest rates, but some analysts wonder if Asia's policy makers should have bigger fish to fry.

Michael Heise, group chief economist at Allianz, noted last week that Asia's economies have seen a solid recovery.

"Trade is one reason why the Asian economy has recovered. The other reason is a little more problematic and it's the credit cycle," he said, pointing to an "enormous" debt build-up across the region, including China.

He noted that between 2007 and 2016, private sector debt, including households and non-financial corporates, rose by around 90 percentage-points of gross domestic product (GDP) in China and around 70 percentage points in Singapore.

"In the short term view, this was good news as it prevented the halt of demand and the weakness of the economies, but in the long term, it raises the question, is it sustainable," Heise asked. "Monetary authorities worldwide should start giving more weight to the issue of financial stability in contrast to pure inflation," he said.

Inflation globally has remained muted, despite policy makers' best efforts to goose it higher with low interest rates and, in some cases, quantitative easing (QE) programs.

In the U.S., the consumer price index for fell 0.1 percent on-month, but rose 1.9 percent on-year, skirting the U.S. Federal Reserve's 2 percent inflation target. A continuing slump in oil prices has dampened consumer prices, with U.S. West Texas Intermediate (WTI) hitting a seven-month closing low on Monday, according to Reuters data.

In Japan, headline CPI rose 0.4 percent on-year in April, up just a tad from March's 0.2 percent rise. Elsewhere in the region, China's CPI rose 1.5 percent on-year in May and Singapore's inflation was just 0.4 percent on-year in April.

Heise pointed to concerns some Asian central banks might also turn on the liquidity taps to combat low inflation, by cutting interest rates further.

"[By] pumping liquidity into a market that already has enough or even lowering interest rates, financial instability even worsens and this loan situation even accelerates," he said. "That would be the wrong reaction."

In a note on Monday, Citi also pointed to expectations* that a "tendency towards downside inflation surprises" meant lower interest rates and low bond yields.

"The downward pressure on yields is easing financial conditions and as yields fall it is also likely to exacerbate the reach for returns that continues to underpin risk assets at increasingly rich valuations," Citi said.

Buying overvalued assets could come back to bite investors later.

Follow CNBC International on Twitter and Facebook.