Wall Street exhaled heavily Friday on news that job creation in both the public and private sectors accelerated and defied some of the recent speculation that the economy had reached full employment.

Beneath the surface, though, trouble lurked.

Despite the strong level of job creation — 222,000 in June, 581,000 over the past three months and 47,000 more in the previous two months than originally reported — wage growth remains stagnant. Even a 4.4 percent unemployment rate hasn't been able to put pressure on salaries, which are growing at just a 2.5 percent rate annually.

Unless conditions change soon, the lack of some healthy inflation is going to start to have consequences.

"I would characterize the market as OK but not great," Michael Stull, senior vice president at job placement firm Manpower North America, said as the Street celebrated Friday's much better than expected June nonfarm payrolls report.

"I would feel a little bit better if some of the contradicting numbers of low unemployment rates and low wage growth were more in line with each other," he added.

That's become a familiar refrain among both investors and economists who wonder why workers aren't making more if the labor market is so seemingly tight. Average hourly earnings rose just 0.2 percent in June, representing a 2.5 percent annualized gain, down from 2.8 percent in February and in line with where the year began.

High rates of inflation are generally bad for economies, but a moderate pace is considered healthy, while deflationary environments are to be avoided at all costs. The Fed would like to see a little faster bit of inflation, especially in places like wages. But so far it's not really happening that way.

Construction salaries are up just 2.2 percent and manufacturing barely 2 percent, though leisure and hospitality pay has risen a comparatively robust 4.1 percent, according to Bureau of Labor Statistics data from the past year.

Stull said the same problem continues to vex both workers and employers — a skills mismatch that is keeping qualified workers from taking lower-paying jobs and employers from hiring aggressively in a labor pool they believe is ill-suited for the challenges of more technical positions.

"We need to be rethinking how we develop skills in order to keep the U.S. competitive. We have to integrate education more with work," Stull said. "We need to create the opportunities for people to earn while they learn so they can move into a better job and have better skills."

From a broader economic standpoint, the inflation question gets even stickier.