It was the team's fifth Super Bowl title since February 2002.
Based on the photo, Providence Journal reporter Mark Daniels tallied up the 34 players in attendance.
"No team has been this good for this long", Trump said.
According to a tweet from the Boston Herald's Jeff Howe, Brady's mother has been battling cancer since before the Super Bowl, and the star QB will be spending time with her.
Besides Brady, six members of the team were not expected at Wednesday's event.
Former Patriots cornerback Logan Ryan is also reportedly busy moving to Nashville.
Per Daniels, here is the full list of players who did not travel to the White House.
Reiss tweeted out a statement from Brady where he said he is "so happy and excited" that the Patriots are being honored at the White House.
Numerous players said they would skip the event due to their political differences with Trump even though Brady, coach Bill Belichick and owner Robert Kraft have close ties to the president. In the first such game to go to overtime, the Patriots pulled off a stunning rally from 25 points down to beat the Atlanta Falcons. The press corps burst into laughter as Spicer responded, "I think I've got this but thank you". Tight end Martellus Bennett and defensive end Chris Long, who have since signed elsewhere as free agents, indicated that they wouldn't make the trip because they were not fans of Trump.
White House press briefings usually focus on the administration's policies and the president's plans for the day. He cited a "family commitment" at the time, but there was speculation he declined because of some unflattering comments a spokesman for President Barack Obama made about the "Deflategate" scandal.