"I mean, this is a surreal moment for me," the Avalanche coach said. "I'm going to try not to get emotional, but I already am. We love you guys. Love you."
Bednar was introduced to the podium after the thousands in attendance heard from Denver Mayor Michael B. Hancock, Colorado governor Jared Polis and Avalanche general manager Joe Sakic.
Sakic was the captain of the two previous Avalanche teams to win the Stanley Cup, in 1996 and 2001.
He built the team that won the Stanley Cup this year, going 16-4 in the Stanley Cup Playoffs and defeating the Tampa Bay Lightning in six games in the Stanley Cup Final, including 2-1 in Game 6 at Amalie Arena on Sunday.
"How about this team," Sakic said. "Twenty-one long darn] years. It's been a long time. But we're back. We're back."
The parade followed a route past Ball Arena down 17th Street with a right onto Broadway and into Civic Center Park. Fans lined the streets as players rode on fire trucks, many stepping off the truck to greet the fans along the route.
"What a parade," Sakic said. "That's unbelievable. You can tell the city of Denver has grown in the last 21 years. So many people."
[Video: Check out the best moments from the Cup Celebration
Bednar was choked up as he spoke to them. It was a culmination of six seasons as Avalanche coach, a run that started with an NHL-worst 48-point season (22-56-4) in 2016-17.
He said he appreciated "the level of commitment and trust and patience" that Sakic, assistant general manager Chris McFarland, owner Stanley Kroenke and president Josh Kroenke had in him and his coaching staff.
"They gave me my first chance," he said, his voice cracking.
Bednar went onto thank the families of the players and coaches for their support, his coaching staff and the Avalanche support staff, and the players for their commitment, continuing to fight back the tears as he spoke.
"I couldn't be more proud of these guys," Bednar said when talking about the Avalanche players. "I can't even explain it. I couldn't put it into words. I mean, these guys, everyone has a story, right? Everyone has a story, and I could go through every guy and the sacrifices they made for our team. I'm amazed by every single one of them. I'm so happy for them. I'm so proud of them. I love these guys."
Avalanche captain Gabriel Landeskog was one of several players to address the crowd after Bednar spoke.
Landeskog, now 29 years old, got to the Avalanche when they made him the No. 2 pick in the 2011 NHL Draft.
"The group of guys behind me, I can't even begin to tell you the resiliency, the commitment to win, the determination to win, the attitude," Landeskog said, a Swedish flag draped around his shoulders. "These guys are the best people you will ever meet. It's these guys right here. And guess what? The city of Denver, the state of Colorado, you guys have been [expletive] amazing for the last 10 years. We just want to thank all of you guys for all your support through the tough times, through all the good times.
"As much as I love these guys behind me, this is for you Denver. We [expletive] love you guys."