"I would not associate Jay Powell with craziness. No, no, he comes across, and members of his board, as extremely serious, solid and certainly keen to base their decisions on actual information, and decide to communicate that properly," she said, speaking to CNBC at the IMF and World Bank annual meetings in Bali, Indonesia.
Lagarde made the comment in response to a question from CNBC's Geoff Cutmore about U.S. President Donald Trump. The American leader knocked the Fed on Wednesday for continuing to raise interest rates despite some recent market turbulence.
"I think the Fed is making a mistake. They are so tight. I think the Fed has gone crazy," the president said after walking off Air Force One in Erie, Pennsylvania for a rally.
Lagarde added: "All over the world, it is certainly a good principle to have independence of the central banks and of the central bank governors. Certainly we have advocated that in all countries, and I think that the Fed is no exception."
Although markets overnight turned rocky, Lagarde said she doubted that the IMF's downbeat growth forecast was to blame.
In fact, it was "completely legitimate," and the 3.7 percent growth forecast figure was "nothing to be ashamed of," she said, adding that the IMF took into account global trade tensions, which are starting to have an impact and are eroding confidence.
The IMF said on Monday that the global economy is now expected to grow at 3.7 percent this year and next year — down 0.2 percentage points from an earlier forecast.
"It could be higher," she said. "Personally I would certainly wish that we take all the right policies in order to have more growth: deescalating the trade tensions ... addressing the issues that the system has, and proposing new terms and a new legal framework within trade operators, companies ... the big corporates can trade and can expect the terms of trade is in my view imperative if you want to continue to see growth."
While trade agreements "take much more time" than trade disagreements, Lagarde suggested that agreeing on a process — accepting the path of negotiation and identifying the problems — could "go a long way" to reassuring companies.
Lagarde acknowledged that the apparent slowdown in China was a concern for emerging economies and low income countries that could face slowing demand for their goods.
But, she said, the re-focus on China's domestic economy "isn't something that's new," and it's in line with China's goal to be less driven by exports, and to reduce the imbalance caused by a surplus.
"Moving from an almost double-digit surplus account to 1.5, 2 percent, is partly caused by a refocusing on their domestic market. Now, if that was to accelerate, clearly there would be spillover effects to other countries that are part of the supply chain, through raw materials or the organization of supply," Lagarde said.