KANSAS CITY, Mo. -- New England Patriots quarterback Tom Brady said he was "as excited as he's been in some time" after Sunday's 37-31 victory over the Chiefs in the AFC Championship Game and explained the reason for his overflowing emotion on the field.

"The odds were stacked against us," he said after engineering his 57th career game-winning drive to bring the Patriots back from a fourth-quarter deficit or tie. "It hasn't been that way for us for a while. It certainly was this year. We started off so slow."

Brady added that the Patriots, who were 9-5 after back-to-back losses in December before finishing 11-5, have played their best football in their past four games.

"That was as emotional of a game as I think I've been through, certainly in a long time. ... All the things that kind of transpired over the course of the game. To get a chance to win it there, like we did, and then to pull it off, was just a great feeling," Brady said Monday in an interview with WEEI.

"You play sports for a lot of reasons, but something like that that happened last night was a game we'll all remember for the rest of our lives. Emotions just take over at that point. You're not thinking much. You're just feeling it. I was just so happy for our teammates and coaches and our whole organization. Mr. (Robert) Kraft, Jonathan (Kraft), just everyone who has put so much into our team, our families, everyone that supports us. Our fans. Everyone. It was really a great, great win. Beating a great football team on the road in January, it's just an incredible feeling."

After the Patriots beat the Chargers in the divisional round of the playoffs, Brady had said in a postgame interview on CBS that "everybody thinks we suck and can't win any games." Following the win over the Chiefs on Sunday night, he was asked if he truly believes that or just uses it as motivation.

Brady paused for a few seconds, and never really answered the question, saying, "Yeah."

Brady finished 30-of-46 for 348 yards, with one touchdown and two interceptions against the Chiefs.

"One play here, one play there, could have changed everything," Brady said. "But that's football. I'm proud of our team.

"When you have 70,000 people cheering against you, it's pretty sweet when you win on the road. That's a hard thing to do in the NFL. It's certainly a hard thing to do against the first-ranked team in the conference who has been playing great all year, and has certainly been playing great at home. We knew it was going to take a lot. It took some great plays and some great conversions, and just proud of us getting the job done."

After the game, Brady approached a security guard waiting outside the Chiefs locker room and asked if he could see quarterback Patrick Mahomes, according to ESPN's Jeff Darlington. Brady was escorted into a room, where he spoke briefly with Mahomes. Brady said he wanted to keep the conversation personal and added, simply, "He's a great player with a great team."