SALT LAKE CITY — They are tired, but not ready to lay down.

Kansas State players and coaches alike admitted to getting very little sleep after Thursday night’s double-overtime thriller over Xavier, an NCAA Tournament classic that gave the Wildcats their first berth in the Elite Eight since 1988.

For some, the excitement of the game contributed to their insomnia. For others, it’s the thought of what lies ahead, including today’s 3:30 p.m. West Regional title game against Butler at EnergySolutions Arena.

“I went to sleep at like three in the morning,” said K-State senior guard Denis Clemente, who played 48 of 50 minutes in Thursday’s game. “I kept waking up. I just can’t believe where we’re at right now.

“I’d open my eyes and say ‘That’s for real, what I’m doing right now?’ I kept waking up every 15 minutes, reliving the moment.”

“I really didn’t get much sleep last night,” junior forward Dominique Sutton said. “All the text messaging, the phone calls, people congratulating us. I didn’t go to sleep until 3:30.”

The Wildcats’ ability to bounce back from that emotionally draining, physically exhausting semifinal will be tested today. They’ll have to be at the top of their game against perhaps the hottest team in the country right now.

Butler (31-4) has won 23 consecutive games, including a 63-59 upset victory over top-seeded Syracuse in Thursday’s early game. The Bulldogs are making their first Elite Eight appearance, but did not necessarily fly under everyone’s radar this season.

Kansas State (29-7) was No. 7 in the final Associated Press and ESPN/USA Today regular season rankings. Butler was 11th in the AP, but one spot behind the Wildcats in the coaches’ poll.

Both teams were ranked in the top eight and now are in the Elite Eight.

“You don’t win 23 games in a row by being an average team,” said K-State coach Frank Martin. “They’re good. They’re very, very good.”

The pace of play could be pivotal to either team’s success. Kansas State has scored an average of 80.4 points a game and has scored 63 points or more in every game. Butler did to Syracuse what it’s done all season, limiting opponents to an average of 59.7 points a game.

Only three opponents have scored 70 points or more against the Bulldogs this season. Butler lost all three games to Minnesota (82-73), Clemson (70-69) and Georgetown (72-65).

“They play like us, up in you,” said sophomore Jamar Samuels, the Big 12’s Sixth Man of the Year. “They try to get every loose ball, every deflection, every rebound. We know that’s our type of game so it should be a good game. I know it’s going to be very physical.”

“Defensively they are very underrated,” Martin said. “They really, really congest the paint defensively and make it difficult for you.

“Then what they do that they get absolutely no credit for is how well they rebound the basketball. They pursue the ball when they are on defense and rebounding.”

The Bulldogs start three sophomores, including 6-foot-9 forward Gordon Hayward, who leads the team in scoring (15.3 ppg) and rebounding (8.2).

Having already set school records for wins in a season and advancing deeper into the tournament than any team since 1988, the Wildcats are anxious to take the next step. That would include making their first Final Four appearance since 1964 and the fifth in the program’s history.

“We’re excited. We’re antsy to play,” junior Jacob Pullen said. “Any team would be antsy to play. It’s a big game.

“At the same time, we’re still focused. We fell like we’re taking another step towards where we want to be at the end of our season.”

But first, some of the Wildcats planned to get some rest.

“We’re going in the hot tub later on today and rest our bodies,” Samuels said Friday afternoon. “Stay hydrated. I promise you since seven o’clock this morning I’ve probably drank eight bottles of water. I’ve got to go to the bathroom now. Everybody’s feeling pretty good right now.”

“I didn’t sleep much,” Martin said. “That’s where Sunday is right around the corner. I’ll sleep a lot on Sunday.”