However, there was a dispute over whether the pair discussed who would pay for the Republican nominee's proposed border wall. In the news conference, Trump said payment wasn't discussed. However, afterward Pena Nieto tweeted that he told the billionaire that Mexico would not pay for it.
Trump's spokesperson responded by saying, "It was not a negotiation, and that would have been inappropriate."
However, Davidow told CNBC, "This is the time that you lay it on the table. If you really think you're a great dealmaker, this is the time when you start negotiating the deal. I didn't see any of that."
Things that Trump has been proposing, like payment for the wall, renegotiating the North American Free Trade Agreement and stopping American business from going to Mexico, should have been raised in a "respectful" fashion with Pena Nieto, he added.
As for why the Mexican president would want to meet with someone who appears to be hostile toward the country, Davidow believes Pena Nieto wanted to get Mexico's side out to the American public.
"If you listen carefully to what he said at the press conference, he presented a really cogent picture of the importance of a friendly Mexico to the U.S. but he didn't say it very well. It got lost in the shuffle of the translation and was overwhelmed by the optics of the event," he said.
In a speech later Wednesday evening, Trump ditched the softer tone he employed during his news conference in Mexico. With renewed bluster, he reiterated his vow to make Mexico pay for the wall and outlined his plan to crack down on immigration.
— CNBC's Jacob Pramuk contributed to this report.