After losing Senate seat, Cassidy answers whether he regrets voting to impeach Trump

"I voted to uphold the Constitution. It may have cost me my seat, but who cares?" Cassidy told reporters at the Capitol on Monday. "I had the privilege of voting to uphold the Constitution, isn't that a great thing?"

"You're looking at a man who loves his country, who feels very, very good about how I serve my country and my Constitution and my fellow Americans," Cassidy said. "Wouldn't all of us want to say, I voted to support the Constitution on something momentous? That's the way I feel about it. I'm very pleased about it."

Letlow came in first with 45% of the vote, followed by Louisiana Treasurer John Fleming with 28%. Cassidy came in third with just over 24% of the vote.

Cassidy, in a speech to supporters after conceding, said, "When you participate in democracy, sometimes it doesn't turn out the way you want it to."

"But you don't pout, you don't whine. You don't claim the election was stolen…. You don't manufacture some excuse," Cassidy said in an apparent jab at Trump. "You thank the voters for the privilege of representing the state or the country for as long as you've had that privilege. And that's what I'm doing right now."

Fox News' Paul Steinhauser contributed to this report.