When tweeting about the rescinded invitation Monday night, Trump referenced the protests which saw many NFL players kneeling for the national anthem.
However, in a statement released Tuesday, the White House didn't reference the kneeling controversy.
"Unfortunately, the Eagles offered to send only a tiny handful of representatives, while making clear that the great majority of players would not attend the event, despite planning to be in D.C. today. In other words, the vast majority of the Eagles team decided to abandon their fans," the statement said.
Either way, it was a tactical error, said Fagan, a CNBC contributor.
While Trump is playing to his base, he's not thinking long term and building the unity he needs, she said. Pennsylvania, which Trump won in 2016, is considered a swing state.
"Whether there were 10 players there or 30 there, it's a tight shot. So just thinking of the PR value of it for the White House, they made a huge error," Fagen said.
Plus, the continuing coverage of the cancellation accrues more negativity toward the White House, she said.
On Tuesday, the players' union, The NFL Players Association, tweeted that it was "disappointed in the decision by the White House to disinvite players from the Philadelphia Eagles from being recognized and celebrated by all Americans for their accomplishment."
Philadelphia Mayor Jim Kenney, a Democrat, said that disinviting the players "only proves that our President is not a true patriot, but a fragile egomaniac obsessed with crowd size and afraid of the embarrassment of throwing a party to which no one wants to attend."
There are also disappointed fans who were planning to attend the event, Fagen pointed out.
"He'd look like a big person standing there with whoever showed up, thousand people cheering for the Philadelphia Eagles," she said. "That's a better play for the president than what we're seeing now."
— CNBC's Jennet Chin contributed to this report.