Kraft said he was delighted to be honored by Trump for a remarkable comeback victory that he said echoed the president's own longshot campaign "against 16 career politicians facing odds nearly as long as we faced in the fourth quarter".
According to The Boston Globe, 34 Patriots players were at the White House to visit with Trump.
Galynn Brady, Tom's mother, has been battling cancer and is now in Boston which may be the reason for his inability to attend the event.
Brady came under fire throughout the election for his friendship with Trump, which drew controversy and headlines throughout the campaign.
Amendola declined to attend, citing a family funeral, but tweeted a "thank you" to Trump for giving him a "shout out" after Trump called out his name at the event in the mistaken belief he was there.
New England Patriots star quarterback Tom Brady will not attend Wednesday's White House ceremony with his teammates due to "personal family matters". Things were different this year as more than 40% of the roster (21 of 53) had Super Bowl experience. Trump curiously seemed to avoid mentioning players who were absent, including Brady.
Brady released a statement Wednesday morning, citing "recent developments" and "personal family matters" as the reason for his absence. The president delivered some remarks, coach Bill Belichick issued some words of his own and a lot of pictures were taken on the South Lawn.
"Whether trying to win a Super Bowl or rebuilding our country there are no days off", Trump said.
Several members of the Super Bowl-winning team - including defensive end Chris Long, running back LeGarrette Blount, defensive tackle Alan Branch, linebacker Dont'a Hightower, defensive back Devin McCourty and tight end Martellus Bennett - also have announced that they won't be visiting the White House.
'I'm not going to the White House, ' McCourty, 29, told Time magazine.
One person who definitely won't ever be skipping the White House ceremony is Belichick. "With the president having so many strong opinions and prejudices, I believe certain people might feel accepted there while others won't".
"He persevered to become the 45th president of the United States", Kraft said, and handed over a number 45 Patriots jersey to the Commander in Chief.