Then, instead of ending it there, Reid took a slight departure from the past and wanted to make a statement that no doubt he will repeat countless times between now and Thursday.
"I'm going to tell you this right now. It's not about me. It's about our football team," he said. "That's the way it's going to remain throughout the next few days when we have the opportunity to play them."
So not much has changed with Reid, other than he's changed the entire culture of last year's 2-14 unit and provided the Chiefs with renewed confidence while revitalizing an entire region.
He still, however, has the same mannerisms in news conferences.
After opening by giving a brief injury update, Reid uttered the famous words to reporters that were heard so often in Philadelphia: "Time's yours."
Reid expressed his gratitude to his team for the way it fought - and for good reason. When Dallas got to within 17-16 on a 53-yard field goal by Dan Bailey with 3 minutes, 50 seconds left, Kansas City ran all but the final 16 seconds off the clock.
Before Dustin Colquitt's punt that pinned the ball on the Dallas 4-yard line, the Chiefs had nine plays, eight of which were runs.
The pass-happy Reid had the Chiefs run the ball 25 times, while quarterback Alex Smith attempted 36 passes.
So Reid could be adapting, especially after his last two seasons in Philadelphia produced a 12-20 record.
A Kansas City region that had become apathetic toward its team has turned hog wild over the Chiefs. Sunday's crowd was 76,952. It was the largest home crowd since Nov. 11, 2007, when the Chiefs drew 77,368 for a game against Denver.
The Chiefs wore all-red uniforms for the first time in their history. And as usual, it was a red-clad stadium full mostly of Chiefs fans, with a few Cowboys intruders.
The players asked Reid if they could dress in all red, and he got approval from general manager John Dorsey.
So the entire afternoon was a red-rocking event with a crowd that kept the decibel level at the highest of pitches.
"The crowd was unbelievable today," Reid said. "They just made it about impossible for the Cowboys to hear."
Reid is the main reason for all this noise. He seems reenergized, and the fans have jumped on his back. And so have the players, such as safety Quintin Demps, who entered the league with the Eagles in 2008. This is his first year in Kansas City after three in Houston.
"Sometimes a new start is good for people," Demps said. "That is what you see in him. He is fresh and ready to go, and he is hungry, just like his team."
While Reid is reviving his career, so is Smith. Acquired from San Francisco after he lost his job to Colin Kaepernick, Smith is thriving in the early going. Against Dallas, he threw for 223 yards, two touchdowns, and no interceptions, and was Kansas City's leading rusher with 57 yards on eight carries.
The new quarterback and coach converse after every play in practice, every series in the game.
"For me it's a blessing to have a coach of his caliber, and to be able to have that instant feedback every single play has been good," Smith said.
There are many reasons for the Chiefs' early turnaround. But whether he likes to admit it, Reid is driving this bus - even if he insists it isn't about him.
Contact Marc Narducci at email@example.com. Follow @sjnard on Twitter.