Americans are paying more for health insurance this year over last — but the increases are relatively modest.

That's according to a major survey out Tuesday from the Kaiser Family Foundation.

Insurance premiums rose 4 percent in 2013, pushing the average yearly cost of a work-sponsored family plan above $16,000. On average, workers are paying about $4,565 of that.

Kaiser Family Foundation CEO Drew Altman says insurance premiums rose meagerly, despite claims that health-care reform could jack up prices.

"Critics of Obamacare will have a much harder time blaming big premium increases in employer insurance on Obamacare this year because there aren't any big premium increases," Altman said.

He says that doesn't mean workers aren't feeling the pinch.

"You can understand why average people just wouldn't perceive it that way," Altman said. "They still feel the pain of health-care costs and worry about it a lot."

That's because wages remain flat and larger deductibles are more common, he said.

Still, Altman says, the small rise in insurance premiums means employers are unlikely to take drastic measures in pursuit of savings.

"It's not an environment where they should be dramatically cutting workers' benefits, which is a message for working people out there," Altman said.

The survey of more than 2,000 employers, large and small, found over 90 percent of companies with 50 or more workers offered health benefits this year. Overall, 57 percent of firms offer health plans, which is about the same as the last two years.