After a mixed and perhaps even confounding jobs report took a bite out of stocks, traders and strategists say the era of low volatility and effortless rallying could finally be drawing to a close.

"There's definitely a different tone in the market this year as compared to last year," Peter Boockvar, chief market analyst at the Lindsey Group, said Friday. "We got a disappointing jobs number, but people still think the Fed is going to taper, despite an uneven recovery."

If this were 2013, Boockvar added, the market would have rallied on a weak number because it would have meant the Fed was going to continue to do what it had been doing.

On Friday, the Bureau of Labor Statistics released a jobs report that read like a "good news, bad news" joke. Total nonfarm payroll employment increased by 74,000, far short of economists' expectations that some 200,000 jobs were created. But while most economists expected the unemployment rate to stay put at 7.0 percent, it actually dipped 6.7 percent, the lowest since 2008.

Theories on what caused the weak number varied, with most economists suggesting that bad weather must have played a role, but that doesn't explain the entire drop from November's 241,000 new jobs (revised up by 38,000 in Friday's report).

"I think there's going to be weather-related anomalies in the next few jobs reports as well," predicted Jim Iuorio of TJM Institutional Services. "So the lack of clarity is going to cause people to trade defensively."

(Read more: Fed officials could ignore ugly jobs report—for now)

For Jeff Kilburg of KKM Financial, the report could signal more shaky markets ahead.

"I think we should see more and more volatile numbers, which will translate into more and more volatile markets," he said.

Volatility was certainly muted in 2013. The CBOE Volatility Index never reached higher than 22 in 2013, which was a big contrast from the 48 reading seen in 2011, much less than the high of 90 in 2008. And last March, the VIX—which measures expected volatility and is sometimes referred to as the "fear index"—touched a six-year low.

For Boockvar, what he calls the "Teflon market" could turn stormy in 2014, even if economic data continue to improve.

"Let's say that today's number is good and the economy is good in 2014. Well, if the Fed is ending QE and interest rates go higher, that's a headwind," Boockvar told CNBC.com. "You could have simplified 2013 and said the rally was due to Fed money printing. Well, if that reverses in 2014, that could be the sole driver of where stocks close this year, too."

(Read more: Dismal jobs data won't alter Fed's taper: Goldman)

The Fed announced in December that it will begin to roll down the $85 billion monthly bond-buying program by $10 billion per month and that it plans to continue tapering through 2014. It added that it will "closely monitor incoming information on economic and financial developments in coming months and will continue its purchases of Treasury and agency mortgage-backed securities… until the outlook for the labor market has improved substantially."

For Boockvar, a situation in which the Fed exits its quantitative easing program while the economy experiences light job growth could prove the worst of both worlds.

"People could get worried if the Fed is going to reduce QE while the U.S. economy is growing. We're adding jobs, but there's still a sense of fragility to it," Boockvar said. "Of course, there's never going to be something written on their foreheads that says 'This is the time to end QE.' There will never be a good time."

(Read more: Wells Fargo bear: Brace for a risky, volatile year)

On the other hand, Brian Stutland said the "good-news-is-bad-news trade" could remain intact, at least for now.

"The jobs report is a little mixed, so it sends a signal the Fed will have to wait a bit to continue tapering," said Stutland, managing member of the Stutland Volatility Group. "As we get towards summertime, sure, there will be more uncertainty about what the Fed will actually do. You can expect more volatility in May or July. But volatility will be muted over the next couple of months."

—By CNBC's Alex Rosenberg. Follow him on Twitter: @CNBCAlex.