The Spahn Award is presented annually to the best left-handed pitcher in Major League Baseball and is based on a pitcher's wins, strikeouts and ERA.
Sabathia had 197 strikeouts, 19 wins and a 3.37 ERA during the 2009 season, earning honors as the MVP of the American League Championship Series in his first season under a seven-year, $161 million contract with the Yankees.
"It takes a lot of pressure off when you play with great players," Sabathia said Tuesday, according to The Associated Press.
"Just being around those guys and them having experience of being in the postseason and being on a championship run, it definitely gives you a calming feeling to be able to be around those guys every day and know what it feels like to win a championship."
The award is named after Oklahoman and National Baseball Hall of Famer Warren Spahn, who holds the Major League Baseball record of 363 wins as a left-handed pitcher. Sabathia credited his teammates with allowing him to enjoy the whole season, start to finish.
"It takes a lot of pressure off when you can just go out and know that if you do your job and worry about what you have to do, then those guys are going to take care of the rest," Sabathia said.
"Every game I started this year, I didn't feel like I needed to go out and throw a shutout or go out and be perfect. Just keep the game close, and hopefully my team is going to score enough runs to win."
Greg Spahn, son of the late Warren Spahn, said Sabathia is closing in on Randy Johnson's record of four consecutive award wins from 1999-2002.
"It's important to note that CC is demonstrating the same consistency that my dad did throughout his career," Spahn said. "Great pitchers are all about being able to do it year after year."
Hall of Famer Ferguson Jenkins was also on hand for the event. Spahn Award chairman Bill Hickman said it was a pleasure to welcome Sabathia back to Oklahoma City for this year's award presentation.
"CC Sabathia is a world-class athlete and also an all-round class act," Hickman said. "His gracious participation in the past two Spahn Award galas has raised Oklahoma City's profile as a big league city and enriched even more the legacy of baseball legend Warren Spahn."
Yankees pitchers and catchers will hold their first official workout on Feb. 18 at George M. Steinbrenner Field in Tampa, Fla. Sabathia told the AP that he thinks New York's offseason moves have made the team "a little better" than the 2009 version.
"It makes you want to go back and do it again," Sabathia said. "I'm itching to get to Spring Training, itching to get started, itching to get to see the guys and just try to do it again.
"Being on that big stage and knowing that the Yankees are committed to winning -- going out and getting a [Curtis] Granderson, going out and trading for another pitcher, Javy Vazquez -- it just makes you feel good that the organization's committed to winning even after you win a World Series," he said.
Past Spahn Award winners include: Sabathia (2007-09); Johan Santana (2004, '06); Dontrelle Willis (2005); Andy Pettitte (2003); and Johnson (1999-2002).
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.