Delta Air Lines CEO Ed Bastian told CNBC Friday that he believes Boeing's delay in assuaging public concerns following the grounding of the aircraft maker's 737 Max jets made things worse.

"I think that delay caused a lot of concern in the consumers' eyes," Bastian told "Squawk Box" co-host Andrew Ross Sorkin in an interview from Atlanta. "When you have a crisis like this, it's going to be newsworthy. And unfortunately, as I said, since they didn't get out far enough in advance of the story, the story was told about them rather than being able to manage the story."

However, Bastian also praised Boeing as a "great American company" with phenomenal engineering talent, saying he'd fly on a 737 Max. Delta does not have any its fleet.

American, United, and Southwest are the U.S. major airlines that fly 737 Max models. Since the mid-March grounding, carriers have had to cancel and re-book thousands of flights.

Aviation authorities around the world grounded the 737 Max planes following the crash of one of the jet in Ethiopia, which came less than five months apart from a crash in Indonesia. The two tragedies killed a combined 346 people.

After French and Ethiopian authorities said that data extracted from the black boxes showed similarities between the two crashes, Boeing chief Dennis Muilenburg publicly stated the company's "relentless commitment to make safe airplanes even safer." The statement came eight days after the second plane went down.

Boeing has faced criticism over the past few months over its response to public concerns. In March, Argus Research downgraded the plane maker to hold from buy, citing the company's management following the second deadly crash. "Boeing management has not been particularly pro-active in its response, and we think the shares are subject to downward pressure as the investigation plays out in the news."

Last week at a conference, Muilenburg apologized to the victims' families and addressed the public's concerns, as the company is gearing up for a potential August return of the jet.

"We know ... that the public's confidence has been hurt by these accidents and that we have work to do to earn and re-earn the trust of the flying public, and we will do that," Muilenburg said. "We are taking all actions necessary to make sure that accidents like those two ... never happen again."

Investigators believe the jet's MCAS flight control system, which automatically pushes the plane's nose down to prevent a stall, was involved in the two crashes. Boeing has said it completed software changes to the system to make it less powerful but the company has yet to validate it through recertification.