"It's basically the first summer Friday. It's before a long weekend. She hardly strays from her FOMC colleagues in normal times. She said we're still on track to raise rates," said John Canally, strategist and economist at LPL Financial. "She didn't say we're going to tighten soon or in June, so I think that leaves September or December."
Traders had speculated that Yellen would have to address the move higher in consumer prices because inflation is one of the Fed's main issues. They said if the pickup in consumer inflation continues, it would be key in determining whether the central bank will need to move sooner to raise rates.
Treasury yields moved higher after CPI, while the yield curve flattened—indicating the market believes a rate rise could come sooner. According to RBS, fed funds futures are now giving 45 percent odds for a Fed rate hike in September, up from a perceived 35 percent chance last week.
After Yellen's afternoon comments, yields stayed roughly in the same range they had been trading in, and stocks gained slightly but were still mostly lower on the day. The dollar index moved higher, adding 0.2 percent after her remarks.
"(CPI) was a gain, a bigger-than-expected gain, and there's been a steady gain in core for the last few months, so in the near term it certainly is influential and brings on the ever-increasing risk of a Fed move. But I don't think we need to change the odds very much," said David Ader, Treasury strategist at CRT Capital.
Yellen spoke in Rhode Island to the Greater Providence Chamber of Commerce on the economy, and she did not take questions.
Read MoreStockman: Stocks and bonds will 'crash soon'
Ader said he hoped to get insight into whether the Fed was concerned about the rise in core inflation or whether it was looking elsewhere. Yellen did give a nod to labor market improvement, and said there were some encouraging improvements to wage growth this year. However, wage data in the CPI on Friday showed zero movement.
Traders had also been anxious about the timing of Yellen's comments, delivered during pre-holiday trading and on a day when some markets close early. Chicago pit trading in foreign exchange and interest rates futures closed early, at 1 p.m. ET, just as Yellen started to speak. But electronic trading remained open. The Treasury cash market was to close early at 2 p.m. ET, and stocks were to remain open until 4 p.m. ET, as usual.
"I think the market has adjusted in anticipation. Yields are higher at the front end by 4 basis points, implying that she'll be more hawkish, but the benchmark 30-year is down on the day. People are betting there's going to be a flatter curve," said Ader ahead of Yellen's speech. "The best-performing issue is the 30-year so if you think the Fed might hike, that's supportive of the back end, relative to the front end."
Tyler Tucci, RBS short-term markets and derivatives strategist, said according to his firms' calculations, fed funds futures Friday morning showed a 100 percent chance for a 25-basis-point Fed rate hike by December. The odds had been as low as 88 percent for December recently after some traders placed bigger bets on January for the first increase.
Art Cashin, director of floor operations for UBS at the NYSE, said the bond and stock markets had different interpretations of the importance of the CPI number.
"Stock guys shrug it off, pointing to distort that is primarily health cost (government related). Bond types see it as somewhat inflationary and fed fund futures move for an earlier Fed liftoff and bond yields rise. Gold seems to side with stock types," Cashin wrote in a quick note.
Ward McCarthy, chief financial economist at Jefferies, said one factor pushing up CPI was rent, and the other inflation data have not been strong enough to change his view that the Fed will hold off on rate hikes until December.
"The bottom line is there's very little signs of inflation of any type. It's a think day. Hope springs eternal. People want to get the Fed off zero. Numbers like we saw today are not going to do that," McCarthy said, noting the decline in last week's PPI and drops in import prices.
But yet, the markets wonder how much the Fed, stating it is data-dependent, will take notice of this one CPI reading.
"All of a sudden, we have back-to-back core CPI advances of 0.23 percent and 0.26 percent in March and April. I certainly do not expect core inflation to be that firm every single month, but I have to wonder how many more of these Fed officials will need to see before they stop worrying about deflation," wrote Stephen Stanley, chief economist at Amherst Pierpont Securities.
Read MoreEconomist says Fed policies could lead to disaster
"A 0.3 percent increase in the core CPI is such a rare event that it holds considerable shock value, even though the unrounded gain was 'only' 0.256 percent. In fact, there have only been four 0.3 percent rises in the core CPI since the financial crisis, and each of them was 0.25 percent or 0.26 percent unrounded. The last time we had a larger monthly increase than 0.26 percent was January 2008," he wrote.
JPMorgan economists, in a note, said they do not expect to see the CPI translate into a gain in the core PCE, the Fed's preferred inflation measure because of the influence of health-care costs.
Medical care in the PCE index is based on inputs from the producer price index, which were softer than CPI data. JPMorgan expects the core PCE to be up 1.3 percent over a year ago.
As for CPI, they noted that medical care services rose 0.9 percent, helping lift core services, up 0.3 percent, the highest since June 2008. Rent measures also gained, with owners equivalent rent rising 0.28 percent. Airfares fell for a second month, losing 1.3 percent.