What did Iran want to accomplish with its attack against bases in Iraq where American troops are stationed, and how will the U.S. respond? Those were arguably the most pressing questions Wednesday after the overnight missile strikes.

Retired admiral Sandy Winnefeld, former vice chairman of the Joint Chiefs of Staff and CBS News military and homeland security analyst, told "CBS This Morning" Iran was playing to four different audiences with its strikes, the first of those being the United States.

He said Iran wanted to say, "'Hey we can hit you guys, and by the way, we didn't hurt anybody so please don't start a war with us that we would lose.'"

The second target audience, according to Winnefeld, was the Iranian people, "and they can say anything they want to to that audience," because the regime so closely controls media and the flow of information inside the Islamic Republic.

Iranian state television has reported the missile strikes killed dozens of American personnel, but there have been no credible reports of American casualties. Winnefeld said the Iranian claims were just posturing — an internal message to show Iran had taken "hard revenge."

The third audience, in Winnefeld's eyes, is the international community. On that front he said Iran wants to show that it carried out the attack legally, in self-defense and they don't want to attract animosity from the rest of the world.

"And the fourth audience, of course, is the regional audience," Winnefeld said.

"'Please don't help the Americans retaliate for this. And by the way why don't you kick them out of the region,'" is what he believes Iran was trying to convey to regional players.

Winnefeld said the attack was "carefully calibrated," with Iran using increasingly accurate ballistic missiles which "probably hit pretty close to what their targets were."

"This is a big sprawling airbase. Mostly desert," Winnefeld said. "They could have targeted these missiles into remote areas to avoid any possibility that an American could be killed. Or they might have done what we would've done, and that is perhaps target aircraft on the ramp, but not barracks or places where there would be a lot of people."

Winnefeld said the U.S. had three basic options as to how it would respond.

"One would be a disproportionate response, which the president alluded to in previous days, but didn't sign up for necessarily. And I don't think that's what he will do. Certainly not what I would advise," Winnefeld said, referring to Mr. Trump's weekend threat to target 52 sites inside Iran, including "cultural sites."

A proportional response could include the U.S. targeting Iranian missile sites, storage and handling facilities or command and control centers, he said.

"But there are a lot of problems associated with that option as well," Winnefeld said.

"The third is essentially to let this go," Winnefeld said. "And underneath you sort of have a tacit agreement with Iran that says 'We got our's, you got your's, by the way we think we might've got the better end of this thing.' And above the line you can tell the international community, 'Hey look how restrained we were and look how much of a menace this Iranian country is. And why don't you climb on board with sanctions and the like?'"

At the same time, Winnefeld said the U.S. could send a strong message to Iran that its proxy war is over.

"That's how this whole thing started," Winnefeld said, alluding to the steady string of small-scale attacks by Iranian-backed groups in Iraq targeting U.S. installations, which culminated with the attack on a base in Kirkuk at the end of December that killed a U.S. contractor.

Winnefeld said the circumstances on Wednesday morning were an opportunity for the U.S. to say, "'we're not going to let you have your proxies hit us anymore and we'll go after them if you do and we'll also go after you.'"

Winnefeld noted that while he believes Iran's direct military response to the U.S. is over, there could still be further covert retaliation.

"I do think that the (Iranian) proxies in Iraq do want a piece of this action. So it's not a good time to be complacent about self-defense for our troops. But that's the real question mark," Winnefeld said. "Where do we go with the nuclear program and where do we go with covert action from Iran?"