Early in her address to graduating Yale students at Sunday's Class Day, Hillary Clinton reached behind the lectern, pulled out a traditional Russian ushanka hat, and held it aloft.

"I mean, if you can't beat 'em, join 'em." she said as the audience laughed and applauded.

The Russian hat gag, a nod to the student tradition of wearing extravagant headgear during Class Day, set the tone for a wide-ranging speech in which Clinton alternately cracked jokes about her loss to Donald Trump in the 2016 presidential election and warned Yale's Class of 2018 that "we are living through a full-fledged crisis in our democracy."

"There are certain things that are so essential they should transcend politics," said Clinton, who never mentioned Trump by name during her address. "Waging a war on the rule of law and a free press, de-legitimizing elections, perpetrating shameless corruption, and rejecting the idea that our leaders should be public servants undermines our national unity."

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Clinton admitted that she still thinks about her defeat by Trump: "No, I'm not over it. I still think about the 2016 election. I still regret the mistakes I made. I still think, though, that understanding what happened in such a weird and wild election in American history will help us defend our democracy in the future."

"Today, as a person, I'm OK," Clinton added. "But as an American, I’m concerned."

The former first lady, secretary of state, New York senator and 2016 Democratic nominee for president also threw in a call for "common-sense gun safety legislation as soon as we can get it" during a brief discussion of Friday's mass shooting at Santa Fe High School in Texas.

"You don’t need to experience gun violence to know that when a teenager in Texas who just survived a mass shooting says she’s not surprised at what happened at her school because, and I quote, ‘I’ve always felt like eventually it was going to happen here too,’ we are failing our children," she said. "So, enough is enough."

Clinton, who graduated from Yale Law School in 1973, cracked some jokes as well. She told students that she was thrilled for all of them, "even the three of you who live in Michigan and didn’t request your absentee ballots in time." She also joked about her audition to join Yale's famous Whiffenpoofs singing club, saying she had buried the tape "so deep that not even Wikileaks will be able to find it."

She continued, "If you thought my emails were scandalous, you should hear my singing voice."

Class Day is celebrated at Yale on Sunday the day before degrees are handed out. It includes the awarding of academic, artistic, and athletic prizes and the major address of commencement weekend.

It also includes such traditions as the planting of the class ivy, awarding top academic and athletic prizes to students, and the singing of Yale's "Bright College Years" while waving a white handkerchief.

The Associated Press contributed to this report.