“Trump went in tough with sharp elbows and then came out saying ‘I’ve succeeded and here we go’ and off to the next place,” he added. “I don’t think that … the allies have any intention to do more than they want to do and at the end of the day nobody else can do anything about it.”

Jacobs doesn’t think Trump’s tough talk is a negotiating tactic to get allies to up their spending.

Trump berated allies during the two-day meeting this week for not spending enough on defense of the alliance. He emerged declaring victory, saying the other members agreed to his demands to increase spending. However, French President Emmanuel Macron disputed Trump's claim .

President Donald Trump speaks to the media at a press conference held after the 2018 NATO Summit on July 12, 2018 in Brussels, Belgium.

Trump also slammed Germany at the summit, claiming the country is being “totally controlled” by Russia. He was referring to oil and gas deals he says have given Moscow too much influence over the Continent’s largest economy.

Jacobs said Germany can do whatever it likes when it comes to oil and gas.

“We’re an enormous producer of both of those commodities,” he pointed out. “It’s a free market and Germany can buy it from whomever it pleases. That has really nothing at all to do with mutual defense, which is what NATO is all about.”

The president is also under fire from those within the Republican Party. On Thursday, Sen. John McCain sharply criticized Trump’s appearance this week, calling it "disappointing, yet ultimately unsurprising."

"There is little use in parsing the president’s misstatements and bluster, except to say that they are the words of one man," McCain, a frequent critic of Trump, said in a statement. "Americans, and their Congress, still believe in the transatlantic alliance and [NATO], and it is clear that our allies still believe in us as well."

On Wednesday, former Air Force Secretary Deborah Lee James told CNBC that Trump’s constant use of allies as “punching bags is likely to backfire because their own domestic audiences will expect them to more and more stand up to our President Trump.”

The White House did not immediately respond to a request for comment.

— CNBC’s John Schoen and The Associated Press contributed to this report.