"It's hard to put myself up to those levels with Randy and all those people that have won this award," said Webb, who posted a 16-8 record and 3.10 ERA this season. "I'm sure it will take a while [to sink in].
"This whole thing and this whole year has been crazy, crazy, crazy," he added. "It's like every month something's going on and hopefully it's not going to stop here."
The award capped off a year of both highs and lows for the 27-year-old Kentucky native.
Webb and his wife Alicia celebrated the birth of their daughter Reagan in March. He then began the year with a club-record eight-game winning streak.
As the team's lone representative at the All Star Game, Webb posted a scoreless fourth inning, using 16 pitches to retire Derek Jeter, David Ortiz and Alex Rodriguez in order.
On Aug. 27, Webb's close friend and former University of Kentucky teammate and roommate Jon Hooker died in a plane crash when Flight 5191 took the wrong runway at Blue Grass Airport in Lexington, Ky. Hooker, 27, and his wife Scarlett Parsley were married the night before the crash and were en route to their honeymoon.
Webb made his scheduled start Aug. 28 and won his 14th game of the season, allowing three runs over seven-plus innings.
"It's just been an up-and-down year with so many events that we haven't had time to sit down and just look back and relax," Webb said. "It's been crazy this offseason. I haven't had a chance to really sit down. Hopefully when this dies we'll have a chance to take a breath."
But it doesn't look like things will be slowing down anytime soon.
Prior to meeting with the media on Wednesday at Chase Field, Johnson called Webb to wish him congratulations while Arizona skipper Bob Melvin was able to chat with Webb on the phone in between interviews.
"My phone has been ringing off the hook since 1:45 [p.m.] yesterday," Webb said. "It's been crazy. All these people that I played with in college, high school coaches, Little League coaches. Everybody has called."
Webb said he doesn't anticipate his neighbors in his hometown of Ashland, Ky., will treat him any differently.
"When I was in the big leagues, they didn't care if I was the Cy Young Award winner or the bat boy," Webb said with a laugh. "Everybody thought of me the same. I don't see them changing very much at all."