Billionaire bond investor Jeffrey Gundlach, the founder and CEO of $135 billion DoubleLine Capital, sees reasons to be concerned about inflation.

"It feels to me like the market started worrying about [inflation] a little bit this week," Gundlach said, later adding it "was the biggest miss on CPI in many years, and maybe even in my whole career."

On Wednesday, the Bureau of Labor Statistics reported that the Consumer Price Index (CPI) jumped 0.8% in April, well ahead of economists' expectations. Excluding food and energy, core inflation rose 0.9% last month, the largest monthly increase since 1982.

On a year over year basis, headline consumer prices surged by faster-than-expected 4.2% in April, the largest gain since September 2008.

Gundlach said DoubleLine Capital's model suggests inflation "is probably going to go higher in the next couple of months" and might peak in July.

"If we keep going higher from there, then I think people are going to be seriously worried because the concept of transitory has everything to do with what they call the base effects," Gundlach said. "It's almost like a Mount Whitney is right next to Death Valley for a reason. The hole in the ground — the dirt has to go somewhere. Inflation got so low that it was a natural rebound."

The investor proceeded to call CPI "kind of a false construct," pointing out, for example, that owners equivalent rent, used to calculate shelter inflation, is up 2% in the last 12 months, but the median home price is up 17%.

"So, if you would replace owners equivalent rent with home prices, the inflation rate actually would have been 8%, year over year," Gundlach said. "So there's reasons really to be worried about inflation."

In recent months, Federal Reserve officials have taken a "transitory" view on inflation.

"I think the Fed is most content when the inflation rate is higher than the bond yields, all the way across the yield curve, which they've managed to accomplish," he said. "So they're trying to make people not scared about inflation by calling it 'transitory.' But how do they know? How does anybody know whether it's transitory or not given the unusual circumstances that we're in?"

Gundlach later observed that Fed officials using the same talking points "starts to sound like some of the mainstream media where every single guest from either the tribe on the right or the tribe on the left has the same talking point."