Former Presidents Barack Obama and George W. Bush delivered eulogies for McCain at the service inside the Washington National Cathedral ... which was packed with dignitaries paying their final respects.

President Obama clearly was addressing Donald Trump without mentioning his name, talking about politics today being small, mean, petty and grounded in insult. He talked about "phony controversy" and "manufacturing outrage." And, as Ivanka Trump looked on, he talked about certain people appearing "brave and tough" when they are actually steeped in fear.

Check out Meghan McCain's eulogy to her dad ... she moves the audience to applause as she explains how the current President can't hold a candle to her dad. She doesn't use Trump's name, but the message is clear.

McCain handpicked 43 and 44 earlier this year as speakers at his funeral, and Obama was reportedly surprised by the invitation. Remember, Obama defeated McCain in their run for the White House in 2008 -- and W bested him in the 2000 Republican primaries.

Although they butted heads with McCain on the campaign trail, there was always respect between the men. McCain famously shut down a voter who called Obama "an Arab" during their 2008 campaign battle.

15 people carried McCain's coffin at the memorial service ... including former VP Joe Biden, actor Warren Beatty, former New York Mayor Michael Bloomberg and former Secretary of Defense William Cohen.

Obviously President Trump was absent from the service -- as was his respect for an American war hero. McCain reportedly made Trump persona non grata when he was making his funeral plans. McCain's former running mate in 2008, Sarah Palin, was reportedly also excluded.

Veep Mike Pence and WH Chief of Staff Gen. John Kelly also attended.

Pence was one of the speakers at McCain's memorial service Friday, where Congress paid tribute as he lied in state at the U.S. Capitol.

McCain's private burial will be held Sunday at the Naval Academy in Annapolis.

Originally Published -- 9/01/2018 6:33 AM PDT