Private-sector employers added 179,000 jobs in May, the fewest in four months, according to the ADP National Employment Report released Wednesday.
The slowdown in jobs growth last month and slower hiring in April than first reported could be a sign that Friday's government report might show an early spring slowdown.
"We have a long way to go even with stronger job numbers," he said.
“The job market has yet to break out from the pace of growth that has prevailed over the last three years.”
May's figure moderated after a strong April rebound following the harsh winter.
ADP revised its April figure to show 215,000 jobs added compared with the 220,000 initially reported.
Meanwhile, the government's April report of private and public jobs gains hit 288,000, the highest level in several years.
Zandi said the growth of the housing market and, in turn, construction is "vitally critical" to the job creation and must pick up pace to ensure the recovery.
Construction added 14,000 jobs, down slightly from 16,000 in April, the report showed.
Another problem is the abundance of slack in the labor market that could take several years to shake out, Zandi said.
Even if the unemployment rate drops to 5.5 percent by the end of 2015, that is only one piece of the labor market's puzzle.
Those who have left the workforce and others settling for part-time work need to find full-time jobs before the market can return to full strength, Zandi said.
"There's a lot of slack in the labor market, and it will take awhile to absorb," Zandi said. "Until then, wages gains are likely to be subdued."
Still, the report showed that jobs growth was broadly distributed among size and type of employer with small business adding the bulk of workers at 82,000.
Manufacturing added 10,000 jobs in May, up from April’s 2,000 and the largest number since December.
ADP said most of the slowdown came in professional and business services, adding 46,000 jobs, down from 75,000 in April.
Service-providing employment rose by 150,000 jobs in May, fewer than the 194,000 in April.