In his eulogy, Simpson said Bush "often said when the really tough choices come, it's the country, not me. It's not about Democrats or Republicans, it's for our country that I fought for."
Simpson told CNBC there were two gems he and his friend lived by: "Hatred corrodes the container it's carried in" and "humor is the universal solvent against the abrasive elements of life."
"They ought to learn this around this joint," said Simpson, speaking from the nation's capital shortly after the funeral ended.
However, he insisted he was not targeting anybody, only reflecting on Bush's life.
"There's too much targeting going on around this place," he said.
"Life is really not all real chaos and 24-7 news," he added. "It's called silence and meditation and reflection and, for God's sake, it's clarity. It's not about complexity and confusion. You've got to sort out the crap. It'd be a good thing for them to start doing. That's good for the world."
Bush's funeral brought President Donald Trump and former Presidents Barack Obama, Bill Clinton and Jimmy Carter together in the same row at the front of the National Cathedral. It was a moment that some called extraordinary for the basic level of civility shown during this tumultuous time in politics.
"It is still nice to be kind and decent and you can still be tough and ornery and partisan. God knows I am," Simpson said. "But down at the bottom of bowels in your gut, you've got to have manners and you've got to have love and that's tough for people even to admit in these times."
WATCH: The most moving moments from President George H.W. Bush's funeral