"You've taken away the threat of rate hikes," said John Briggs, RBS head of strategy.
Clemons said the Fed was clearly responding to sluggishness in China but generally pinned it on international developments in its comments. "I think this pushes it off until October. If between now and October, some of these developments abroad to which they refer—China—calm down, I think that will pave the path for an interest rate increase in October. It pushes out the inevitable," said Clemons.
The Fed raised its GDP forecast to 2.1 percent growth in 2015 but cut it for 2016—to 2.3 percent from 2.5 percent. It also lowered 2017 growth to 2.2 percent from 2.3 percent. Its 2015 inflation forecast fell from 0.8 percent in June to 0.4 percent, while 2016 slipped to 1.7 percent from 1.8 percent.
Read More Did the Federal Reserve make the right decision today?
The shorter end of the Treasury curve rallied hard, with yields falling in an inverse move. The two-year was yielding 0.72 after holding above 0.80 percent for most of the day.
Stocks bounced around and briefly turned negative before trading became choppy. The market was slightly higher ahead of Fed Chair Janet Yellen's news briefing at 2:30 p.m. ET, rallied during her remarks and then closed mixed.
"It just prolongs the uncertainty with which we've been living," said Clemons. When the Fed ultimately raises rates, it will be a positive, he said. "It will take the uncertainty off the table."
Read MoreWhen do you think the Federal Reserve will hike rates?
Mesirow Financial's chief economist, Diane Swonk, said the most-telling aspect of the Fed release was the downward revisions in its economic forecasts and inflation outlook, signaling real concern about the impact of China and foreign exchange volatility on the U.S. economy.
Two Fed officials shifted their forecast for a first rate hike into 2016 bringing the total for next year to three. One member wants the first rate hike in 2017, and 13 remained in 2015. "The most important thing here is the doves grew in ranks and their voice got louder than the hawks," she said.
Read MoreHere's what changed in the new Fed statement
"It's very important we have out there now that the Fed might not move in 2015. It's a probability now much higher than it was before. It was going to be tough to get all their ducks in a row by December. They'll still want to get there, but uncertainty is not something you want to raise rates into," Swonk said.
"Every central bank in the world is ultimately worried about getting inflation too cold or too hot, and right now the porridge is not just right."
Thursday's Fed decision was one of the most anticipated in years, since there was a reasonable chance the central bank could have raised rates were it not for its concerns about international developments. About half of Wall Street's economists expected a rate hike, even though market expectations were just about 30 percent.
The Fed last raised rates nine years ago, and it has held the fed funds rate at zero to 0.25 percent since December 2008.