"In some ways you could argue that Rajan has made his first mistake before he's formally started in not being active enough in reassuring markets about his commitment to stabilize the rupee," Robert Prior-Wandesforde, director for Asia economics at Credit Suisse, told CNBC Asia's "Squawk Box."
"The market has been crying out for some jaw-boning from him. I hope the RBI and government together set currency stability as their chief priority. If they do not, the rupee could continue to drop, inflation will rise and rates will be forced higher," he added.
The middle of a storm
The rupee traded at around 68 per dollar on Wednesday, close to last week's record high of 68.8. Analysts say that steps such as last week's decision by the RBI to provide dollars directly to state oil companies have helped stabilize the battered rupee, but more needs to be done to restore confidence.
India's wide current account deficit and the slow pace of economic reforms have put the country at the center of the storm sweeping through emerging markets, as investors brace for an unwinding of the U.S. monetary stimulus that has pumped liquidity into global markets in recent years.
Worries about Fed tapering have led to an exit of cash from emerging markets. India's stock market, for instance, has tumbled more than 10 percent since late July and the broader MSCI emerging markets stock index has shed about 4 percent over the same period.
(Read more: Emerging Asia rout start of a multi-year bear market?)
"The market is saying all the money that flooded into India has been misspent, funding a credit bubble, so when that is being unwound you have to kill domestic demand in order to come back to a surplus," independent economist Andy Xie told CNBC.
"India is facing the same situation as Thailand did 15 years ago when it tried to hold onto growth," he added. "It is very dangerous to change the captain in the middle of a huge storm."