Federal Reserve officials aren't truly concerned about inflation now, as they focus on preventing another economic downturn, says Harvard economist Kenneth Rogoff.

"You've just gone through this epic recession; inflation has been below target for a really long time," he told CNBC.

"If inflation goes above target, [Fed officials] are going to say they care, but they really don't care. The big game here is not to have another double dip, not to cause problems."

Editor’s Note: 5 Shocking Reasons the Dow Will Hit 60,000

The central bank has an inflation target of 2 percent. Consumer prices rose at exactly that rate for the 12 months through July. The Fed's favored gauge of inflation, the personal consumption expenditures price index, climbed 1.6 percent during that period.

While various data indicate the jobs market isn't "super-healthy, it's tighter than you think, and [Fed Chair Janet Yellen] admitted that" in a speech last month, Rogoff said.

Nonfarm payrolls increased 142,000 last month, the weakest gain of the year. That came after six straight months of gains topping 200,000.

Many economists believe the latest jobs numbers will keep the Fed from rushing to raise interest rates.

"It [the report] gives Yellen a little wiggle room to do what she wants to do, and that is end the tapering and not start raising rates anytime soon," Diane Swonk, chief economist at Mesirow Financial, told Bloomberg.

Editor’s Note: 5 Shocking Reasons the Dow Will Hit 60,000

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