Speaking before an event in Oklahoma City on Saturday, the $161 million left-hander said that he is prepared for the heightened demands of spearheading the Yankees' rotation.
"If you ask anybody in my family or anybody that knows me, I don't think there's any outside pressure that could be put on me that I don't put on myself," Sabathia told The Associated Press. "I put an enormous amount of pressure on myself to go out there and perform and expect to win every game, expect to pitch well in every game."
Sabathia was in Oklahoma City to be honored with the Warren Spahn Award, issued to baseball's top left-handed pitcher -- the second consecutive year that Sabathia has won the award.
The trophy is a bronze statue of Spahn, the Oklahoma native who leads all left-handers with 363 career victories. He died in 2003.
"It is a great way to honor my dad's memory, and we're tickled to death to have CC back here again this year," said Greg Spahn, Warren's son. "I've challenged him to come back for a third one, and we hope we can see that happen."
After a midseason trade to the Brewers, Sabathia went 11-2 and threw seven of his Major League-best 10 complete games, leading Milwaukee to the playoffs for the first time since 1982.
Considered the prize of this winter's free-agent pitching market, the 28-year-old Sabathia inked a seven-year, $161 million contract with the Yankees last month, agreeing to pitch in New York after general manager Brian Cashman visited his Vallejo, Calif., home during the Winter Meetings.
Sabathia was introduced along with fellow rotation mate A.J. Burnett in a joint press conference held at Yankee Stadium on Dec. 18.
Before conducting an interview session with reporters in the auxiliary locker room, both Sabathia and Burnett spoke to George M. Steinbrenner on the telephone, with the longtime Yankees owner relaying his hopes for a championship-caliber club in 2009.
"That's what I'm looking for," Sabathia said. "That's a thing that I'm big on, having great team chemistry, and hopefully we can get that in New York."
Thought to be perhaps the final event held at the old facility, the Yankees surprised everyone by landing Mark Teixeira two days before Christmas, trotting him out to the press in January.
Sabathia -- who split last season between the Indians and Brewers, posting a combined 17-10 record with a 2.70 ERA in 35 starts -- said that he believes playing alongside Alex Rodriguez, Derek Jeter and Teixeira will help him to be a better player.
"All I'm going to say is I'm excited to be on a big-market team, and to be able to get where we need to win and know that the organization's going to do that every year, year in and year out," Sabathia said. "That feels good."
Good enough that Sabathia feels the Yankees will stack up in the hyper-competitive American League East, which has seen its landscape change somewhat.
The Rays are the new face on top of the stack, having represented the circuit in the World Series, but Sabathia is also excited about walking to the mound in Fenway Park with the words "NEW YORK" across his gray jersey.
"I'm sure it's going to be a little more harsh, but they're tough anyway. Being in a Cleveland uniform, they were tough," Sabathia said. "I'm looking forward to them being even tougher, me being in a Yankee uniform and hearing some rude things."
Before Saturday night's ceremony, Sabathia said in a press session that he is looking forward to having Mariano Rivera close out games for him.
"To have that bullpen and have just the support of that team, that team is unbelievable," Sabathia said. "To add me and A.J. and put Tex in that lineup, I think it's going to be an unbelievable team. Hopefully we have a special year."
Bryan Hoch is a reporter for MLB.com. The Associated Press contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.