Stocks sold off globally after U.S. stocks turned in a mixed reaction Thursday after two hours of volatile trading. Asian markets were mixed overnight, with the Shanghai up 0.4 percent, but selling gripped European stocks, and the German DAX was down about 3 percent.
Read MoreFed dovishness may have stopped soothing markets
The Fed, in its statement, said: "Recent global and financial developments may restrain economic activity somewhat and are likely to put further downward pressure on inflation in the near term." It also pared back its growth outlook for 2016 to 2.3 percent from 2.5 percent, and cut its inflation forecast to just 0.4 percent this year from an earlier expectation of 0.7 percent.
"We kind of have a consensus that the international economy has problems but the domestic economy is improving, and the Fed now allows us to question that," said Adams.
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The Fed's meeting was the source of much market focus, since it was the first at which there was a good chance the Fed could have moved off of its extraordinary zero-rate policy. But while the market anticipated just a 30 percent chance, economists were more divided, and about half thought there would be a hike.
Fed Chair Janet Yellen stressed that the Fed could still raise rates this year, including at its October meeting. But the market is giving higher odds to December and even higher odds to next year.
"Volatility is not going away, period," said Julian Emanuel, equity and derivatives strategist at UBS. "But it's a bottoming process because the economy's OK, and she (Yellen) went out of her way to tell us the economy is OK. Whether the market bought that is completely another question. The most interesting thing is she singled out business investment, which has been missing in this cycle, and that's good for stocks."
Emanuel expects stocks to stay choppy for a while but he anticipates a fourth-quarter rally, after a period when stocks could test the August lows.
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"When you look at the valuations and you look at interest rates, it's very, very hard to make the bear case for stocks unless you really think China is such a problem that it could infect the U.S.," Emanuel said.
Stocks rallied for two days ahead of the Fed decision, fueled by short-covering and the S&P 500 was a half percent higher for the week. The bond market in some way was just as volatile. The two-year yield was at 0.68 percent Friday morning, after rising above 0.81 ahead of the Fed news. The 10-year was at 2.16 percent.
The dollar index was weaker on the Fed news but came off its lows as the euro traded lower.
"I think it's really kind of interesting that the Fed did not move because they were concerned about the equity market, and now the equity market has gotten trashed," said Arthur Bass, managing director at COEX Partners. "I personally think there's a decent chance we don't see a move until 2016, but I thought that for a while."
Tom Simons, money market economist at Jefferies, said the market will be focused on Yellen's comments at a speech next Thursday and other Fed speakers. "The Fed speaking calendar comes to life, but not as much as it should because there's a lack of clarity," he said. "If they had communicated the rate hike was not a strong possibility, things would be easier to swallow today."
Read MoreFed holds off, markets now bet on 2016
Simons did not expect a rate hike this week, but has been looking forward to one in December.
"If the Fed were just dealing with the U.S. economy in a vacuum, they could have raised rates at any time," he said. "What's been keeping them from doing this is commodity prices.... On the margin, this makes it a little less likely they would go in December. Frankly they were signaling more dovishness than I had anticipated."