Chiefs icon Kelce lost his temper with Reid during a first-half flashpoint in Sunday's Super Bowl, sending the coach stumbling off balance while screaming into his face.
Reid, who has forged a close relationship with Kelce since recruiting him out of college in 2013, later played down the incident.
But in Wednesday's edition of the New Heights podcast Kelce hosts with his brother Jason, Kelce admitted he had been out of line.
"It's definitely unacceptable and I immediately wish I would have took it back," Kelce said on the podcast.
"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, s***' in my head."
Kelce, who is dating megastar Taylor Swift, was gearing up to take part in the Chiefs' victory parade on Wednesday.
The 34-year-old added on his podcast that his outburst against Reid arose from frustration about the Chiefs' faltering first-half performance.
Kelce blew up after being kept off the field for a crucial play which led to a Kansas City turnover.
"It just came in a moment where we weren't playing very well," Kelce said. "I wasn't playing very well and we had to get some s*** 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 s*** 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."
The 6ft 5in tight end added that Reid - who barely responded to Kelce's outburst - would have been within his rights to react forcefully.
"I deserve it," Kelce said. "If he would have cold-cocked me in the face right there, I would have just ate it."
Speaking after Sunday's Super Bowl win, Reid said Kelce's meltdown stemmed from the player's competitive spirit.
"He was emotional today," Reid said of Kelce. "But listen, I've got five kids and I know how that goes. The part that I love is that he loves to play the game, and he wants to help his team win.
"It's not a selfish thing. And I understand that. As much as he bumps into me, I get after him. And we both understand that - he just caught me off balance."
