The 36-year-old, who left PSG at the expiry of his contract in June, said: "I was the only player of the 25 that didn't get a [club] recognition," in an interview with ESPN's Migue Granados.
"It was understandable ... because of us [Argentina], they [France] didn't retain the World Cup."
However, Al-Khalaifi denied Messi's version of events on Saturday.
"As everyone saw, because we even published a video, we celebrated Messi in training, and we also celebrated him in private," Al-Khalaifi told reporters.
"But with respect, we are a French club. It was of course sensitive to celebrate at the stadium. We must respect the country he defeated, his teammates on the France team, and our supporters too."
The Argentina forward joined Inter Miami in MLS in July and lifted his first silverware with his new side, the Leagues Cup in August amid a torrid run of form that has seen the club bolster its chances of reaching the playoffs.