KANSAS CITY, Mo. -- Kansas City Chiefs quarterback Patrick Mahomes draped himself in a parka and clung to the heated bench along the sideline during the overtime period of the AFC Championship Game, trying to stay warm while waiting for a chance that would never come.

Instead, he could only watch as Tom Brady converted three times on third-and-long on his way to the game-winning touchdown and a 37-31 overtime victory that sent the New England Patriots, and not the Chiefs, to Super Bowl LIII.

Maybe that was the most difficult thing about the defeat. The Chiefs had their chances to claim a victory but the one they didn't get -- the NFL's likely MVP with the ball in overtime -- hurt more than anything.

"We have the best quarterback in the league, the best offense in the league, and we have to give him a chance," linebacker Reggie Ragland said.

That's what will haunt the Chiefs until training camp opens next summer -- not some questionable rulings by the officials, not an offside penalty by linebacker Dee Ford that negated a fourth-quarter stop.

"He's hurting," coach Andy Reid said of Mahomes moments after the game's end. "He's a competitive kid, so he's emotional right now. He'll grow from this but it's not easy right this minute."

In that sense, the Chiefs were beaten not only by a faulty defense that allowed 524 yards, but by chance. The Chiefs had won 14 of 19 coin tosses heading into overtime on Sunday but but lost the biggest one of the year.

The way both teams were scoring in the fourth quarter -- the Chiefs won the period 24-14 -- the game may well have been decided when the Patriots won the right to get the ball first.

"If we got the chance, I felt like we were going to score," Mahomes said after he had a chance to compose himself. "No doubt at all. But that's just ifs and buts. ... At the same time, I felt we were rolling.

"It's just how the coin tosses, I guess you could say. It's a thing where [Brady] had a great drive, had a lot of third-down conversions. At big moments guys had big catches for him."

The Chiefs were shut out in the first half for the only time of the season but rallied from their 14-0 deficit to twice take the lead in the fourth quarter. Mahomes threw three touchdown passes in the second half.

But his stat line in overtime was all zeroes and the Chiefs can only ponder what might have happened if the coin had come up tails instead the heads called by the Patriots.

"Seems like anything is possible with Pat," tackle Mitchell Schwartz said. "It feels bad because it feels like we let him down. Hopefully, good things to come. We got a lot of talented players."

That was also a theme in the postgame locker room, that the Chiefs may soon get another shot in an AFC title game.

"We know this can be a building block," Mahomes said. "It could be something that carries us into the future. Right now it's the end, but hopefully it's just the beginning of a long time."

Said Reid: "It's a bright future. We've got good players and we'll get over the hump here. ... We're going to get that son of a gun. We'll bear down this offseason and make sure we get better."

But the Chiefs can't be certain they'll be back in the AFC Championship Game next year or ever. Their previous appearance was 25 years ago, in 1994, and they experienced little but heartbreak in the postseason ever since.

That's why the Chiefs were frustrated about the whims of the overtime coin flip

"It's hard to speculate and say what we would have done if we would have got it first, but ... I feel like we would have [scored]," guard Cam Erving said. "But that's only for imagination now."