Speaking on his 'New Heights' podcast alongside his brother Jason, Kelce explained the situation, admitting that he went too far.
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"I can't get that fired up to the point where bumping Coach and it's getting him off balance and stuff. When he stumbled, I was like: 'Aw, sh*t' in my head."
Angered that Reid had taken him out of the game during the first half, Kelce pushed the 65-year-old so hard on the sideline that the Chiefs head coach momentarily lost his balance, while the tight end continued to shout in his face.
Kelce was eventually pulled away by teammate Jerick McKinnon.
Reid laughed off the incident following the Chiefs' victory over the San Francisco 49ers, telling CBS' postgame show, "He keeps me young. He tested that hip out. He caught me off balance - normally, I'd give him a little bit, but I didn't have any feet under me."
But on Wednesday's podcast, Philadelphia Eagles center Jason said that his brother "crossed the line" and that his yelling in Reid's face too is "over the top."
Travis called the incident a "cheap shot," adding that he wishes he could have taken what he did back.
The 34-year-old explained that Reid came up to him after the incident and didn't have any harsh words for him, even though Kelce expected some.
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"I deserve it. If he would have cold-cocked me in the face right there, I would have just ate it. I would have been like: 'Let's f**king go.'"
Instead, Reid told him that he loves Kelce's passion and that it fired him up even more to get a win for him.
RELATED: Andy Reid addresses heated Super Bowl moment with Travis Kelce
Kelce was supported by another legend of the game in the form of Tom Brady, who said that the encounter was typical NFL "family issues" and something he was a part of regularly.
"Emotions are so high. You are definitely not centered and balanced. You're not in a meditative state at that point," Brady said on the 'Let's Go! with Tom Brady, Larry Fitzgerald and Jim Gray' podcast. "You are fully determined to go out there and to win.
"So I think a lot of the things that are said during the games, people should just let them fly off their back. And I actually think Coach Reid handled it just awesome, like he always does, 'cause he just said: 'I was a little off balance and Travis is such a competitor.' And I love that because it just speaks to his leadership ability."
The incident occurred in the first half of Super Bowl LVIII, during which Kelce was held to just one catch for one yard.
However, by the end of regulation and overtime, Kelce had nine catches for 93 yards and was a key reason behind the Chiefs retaining their Super Bowl crown and winning their third title in five seasons.
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Kelce detailed his relationship with Reid - who he has played his whole career under - on Wednesday's podcast, saying that he has a "certain relationship" with the Chiefs head coach.
"He's checked me a few times, and I just wanted to let him know that I wanted this thing and that he can put it on me and I got him," Kelce explained. "It just came in a moment where we weren't playing very well. I wasn't playing very well and we had to get some sh*t going.
"Sometimes, those emotions get away from me, man. That's been the battle of my career, but, everybody else, I don't give a sh*t what anybody else says. I talked to Coach Reid about it today and we kind of chuckled about it. I couldn't be more proud of being his product on the field, and I couldn't be more proud of where we've come as a team since I got here in 2013.
"I just love playing for the guy, man. And unfortunately, sometimes, my passion comes out where it looks like it's negativity, but I'm grateful he knows it's all because I want to win this thing with him more than anything."
Kelce and the Chiefs will go for an unprecedented three-peat of Super Bowl titles next season.
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