Haley, who's generally done a good job this season of holding his temper in check, made a single comment to McDaniels as the Denver coach held out his hand after the Broncos' 49-29 victory in Denver. Haley pointed his finger at him, turned and stomped away without shaking.
In his opening remarks to reporters on Monday, Haley offered his apology before he was asked about the incident which instantly became a hot topic around the league.
"It sounds like it's become a big deal and I do want to apologize for me not shaking Josh's hand after the game," he said. "I do believe in doing what's right and that was not right. Probably let the emotions of the situation get me too much. And I apologize. I apologize to the fans and to Denver and to Josh."
Haley declined to say what upset him.
"I don't think that's necessary to get into it," he said. "I think it's very necessary that I let everybody know that I would do that over again at the end, and it wasn't the right thing to do."
He said he had not contacted McDaniels to personally apologize.
"I felt like, again, communicating to the majority, and anybody that was watching it, to let them know how I felt and I think that's what's important," he said.
Audio of the brief exchange between the two was provided to The Associated Press by WDAF-TV in Kansas City. McDaniels does not speak but Haley can clearly be heard saying as he pointed at the Denver coach and turned to walk away, "There's a lot of [expletive] being talked about you."
The incident inflamed Broncos fans and is certain to be front and center among Chiefs followers when the Broncos visit Arrowhead Stadium on Dec. 5.
The Broncos roared to a 35-0 lead -- the biggest first-half deficit in Chiefs history. The loss knocked Kansas City into a first-place tie with Oakland in the AFC West.
In his meeting with reporters on Monday, McDaniels said he could not explain Haley's snub.
"I'm not sure about that," he said. "I was proud of the way we played and I have a lot of respect for their entire organization. Obviously, I know a lot of people over there. So, I'm not really sure."
He also said he was not upset.
"It's part of the game. And we all make choices. So."
Aside from being upset about the worst loss the Chiefs (5-4) have absorbed all year, Haley could have been upset at the brutal hit Denver linebacker Joe Mays put on tight end Tony Moeaki during an onside kick in the final minutes. Moeaki had to be helped off the field. There was speculation that Haley was upset at the way the Broncos were laughing on their sideline, and that he felt Denver was trying to drive up the score.
Haley might also have been angry that the Broncos were still blitzing a gimpy Matt Cassel well into the fourth quarter.
When the Chiefs routed the Broncos 44-24 on the same field in last year's regular-season finale, Haley pulled most of his starters in the final minutes and declined to give running back Jamaal Charles an opportunity to break Adrian Peterson's NFL rushing record. Charles was removed from the game needing just 37 yards to do it.