Mike Greenberg weighs in on the mixed fan reaction to Tampa Bay QB Jameis Winston and Patriots QB Tom Brady catching up after the game. (1:47)

TAMPA, Fla. -- New England Patriots quarterback Tom Brady and Tampa Bay Buccaneers quarterback Jameis Winston met in the tunnel underneath Raymond James Stadium following Thursday night's game, sharing an extended conversation that Winston had hoped would happen.

"I just said, 'It was an honor.' I told him thank you. A lot," Winston said after the Buccaneers' 19-14 loss. "That's a blessing, man, to meet someone like that. I dream to be able to be the type of quarterback he is for his team to our team."

ESPN Staff Writer Neat scene as Jameis Winston and Tom Brady catch up as Brady makes his way out of Raymond James Stadium.

Brady, 40, had just finished his postgame news conference, and as he walked toward the team buses, the 23-year-old Winston was waiting for him.

Earlier in the week, Winston had talked about possibly meeting up with Brady, wondering what he would say to him.

The conversation after the game was an extended one.

"Utmost respect for him," Winston said, adding that he preferred to keep what they talked about between them. "He's definitely an inspiration to me and the quarterback position, definitely. Like every young kid growing up with a football in their hand aspiring to be like Peyton Manning, Tom Brady, Joe Montana -- guys of that nature. It was a privilege and an honor to meet him, to look him in his eye, to shake his hand. It felt good. That was another highlight of my night.

"I hate that he beat me, but he beats a lot of people."

Asked his reaction to how highly Winston speaks of him, Brady said, "I feel that same way about a lot of younger players, too. I watch those guys and try to learn from them. When I was young, I learned from the older guys. And now that I'm older, I'm trying to learn from the young guys.

"He's a great young player and he obviously led the team back tonight, and they were very close. He's got a great future."