The audience, which included a who's who of Washington elites, applauded the comment, the Arizona Republic reported.
As millions tuned in to the nationally televised memorial attended by nearly all of Washington's past and present powerbrokers, Trump himself was notably absent - fleeing the capital to head to one of his golf courses in Virginia just as eulogies to McCain were being delivered.
McCain's daughter Meghan McCain delivered a powerful, tearful eulogy, focused on her pride of her father, but peppered with seeming jabs at Trump. Prior to his life in politics, he served as a pilot in the U.S. Navy.
Mr Trump was not in attendance.
Trump chose to head to his Virginia golf course during the service and tweeted his grievances against the Federal Bureau of Investigation and NAFTA throughout the day.
While other speakers, such as former president Barack Obama, kept their inferences to the current administration vague, McCain wasn't shy in demonstrating her distaste for Trump and the bombastic narrative that often surrounds his team. Their pushback to Trump was more subtle than Meghan McCain's but unmistakable nonetheless.
The senator's passing marked the end of a 35-year political career that brought the independent-minded Republican within reach of the White House as his party's presidential nominee. It's a politics that pretends to be courageous and tough, but is instead born of fear. John called on us to be bigger than that. He made us better presidents, just as he made the senate better.
The former president also said that while McCain's tempers would flare, the senator "was just as quick to forgive and ask for forgiveness".
Obama said they "saw our political battles, even, as a privilege, something noble, an opportunity to serve as stewards of those high ideals at home, and to advance them around the world".
McCain's motorcade arrived from the Capitol, where he laid in state overnight.
On Thursday, a memorial service was held in Phoenix and on Friday, a ceremony was held in the US Capitol, where McCain's body was lying in state.
Meghan McCain honours father at funeral service in Washington, D.C. He died August 25 at age 81. During the speech, Obama referred to the maverick senator as an "extraordinary man" who was able to transcend party for the betterment of a nation.
Trump and McCain's contentious relationship worsened after the self-described "maverick" voted down a bill that would have repealed large swaths of Obama's Affordable Care Act. He also noted that McCain "detested the abuse of power", adding "To the face of those in authority, John McCain would insist that we are better than this, America is better than this". John McCain's funeral was more than a remembrance of a man. "We never doubted the other man's sincerity or the man's patriotism".
Trump meanwhile was seen wearing a "Make America Great Again" cap on Saturday morning.
A private service will take place at the US Naval Academy in Annapolis, Maryland, on Sunday, and McCain will be laid to rest in the US Naval Academy Cemetery.
"Back", McCain wrote on the last page of his recent memoir, "where it began".