NEW YORK -- There was some personal satisfaction for CC Sabathia being able to finish off the season with a victory and an ovation from fans at Yankee Stadium.

Inside a quiet clubhouse stood a disappointing reality that for the third time in four seasons, the New York Yankees would be missing the postseason.

Despite 7 1/3 effective innings from Sabathia in Thursday's 5-1 victory over the Boston Red Sox, the Yankees were officially eliminated from postseason contention.

"It's not what we wanted," Yankees manager Joe Girardi said. "It's pretty quiet in there. Probably the quietest I've ever seen after a win. I think guys realize it came to an end tonight. It's difficult. There were some good things that happened but again we fell short and we didn't have a successful season."

Statistically, Sabathia had his best season since 2012, the last time the Yankees won a playoff game. He finished with a 9-13 record but ended with a 3.91 ERA after allowing one run and four hits in his 223rd career victory.

"It was a good season for me," Sabathia said. "Overall to make all but two starts means a lot. It gives me something to build on for next year."

Sabathia began his eighth season with the Yankees as the team's fifth starter but ended it by posting his lowest ERA since 2012 and pitching 179 2/3 innings in 30 starts while only missing two starts in May with a minor groin injury. Sabathia was the ace for his first four seasons when the Yankees won the World Series in 2009 and 21 postseason games but their only postseason appearance since was a loss to the Houston Astros in last year's wild card game.

"You obviously want to have a chance to play," Sabathia said of being eliminated. "We had our chances but fell short."

The left-hander battled through various injuries in each of the previous three seasons but learned how to pitch effectively with a knee brace and a cut fastball to go along with other pitchers. His final display featured eight strikeouts and earned him a standing ovation when he walked the mound after Travis Shaw grounded out.

"It means a lot," Sabathia said. "Especially at home, you want to finish the season good."

Sabathia's final out occurred shortly after Baltimore finished off its 4-0 victory in Toronto. He said he did not know the result until reaching the clubhouse but Girardi said he was aware of it.

"At that point the only thing that became important in a sense was to get CC this win because I thought he pitched really well this year," Girardi said. "I thought he deserved a win."

One of Sabathia's strikeouts came against David Ortiz, who was 0-for-1 with a walk in his final game against the Yankees. . He was lifted for pinch runner Brock Holt after drawing a walk in the fourth and exited to mild applause, mostly from the Red Sox fans in the crowd after getting a standing ovation before his first at-bat."

"CC's and I go way back. CC's a great competitor," Ortiz said. "I have a lot of respect for CC."

Before taking his final at-bats, he was honored in a brief ceremony where he was accompanied by his wife and two children.

Former Yankees pitcher David Cone and former Red Sox teammate Ellsbury presented him with a leather bound book with greetings from various Yankees. Former New York closer Mariano Rivera presented Ortiz with an oil painting of the slugger tipping his hat to fans at Yankee Stadium.

"I don't remember seeing that happen before," Ortiz said. "I did appreciate it. The ceremony was very nice."

"I thought tonight the gift that he received, that leather-bound notebook, might be the most meaningful gift that we've seen and received on this entire year and this tour," Red Sox manager John Farrell said.

Starlin Castro, Jacoby Ellsbury and Aaron Hicks had RBI doubles for the Yankees, who began this season by losing 17 of their first 26 games and dropped 11 of 14 before winning their last four games. Rookie Tyler Austin had a bases-loaded walk and Chase Headley scored on a wild pitch for New York,

Xander Bogaerts homered for the Red Sox, who dropped their third straight following an 11-game winning streak. Boston (92-67) is two games behind the Texas Rangers for the best record in the American League, but one-half game ahead of Cleveland for the No. 2 seed.

Henry Owens (0-2) started in place of Drew Pomeranz (forearm) and allowed two runs and four hits in 4 2/3 innings.

NOTES: A banner reading "Thank You 34" was placed above the intersection of Yawkey Way and Van Ness Street outside of Fenway Park ahead of DH David Ortiz's final regular-season games. ... RHP Masahiro Tanaka threw a bullpen session without difficulties but the Yankees have yet to announce if he will start Saturday versus Baltimore. ... Red Sox manager John Farrell said he wants to get all his relievers at least one appearance in the final four games and that includes LHP Drew Pomeranz (forearm), who had a bullpen session and did not have any physical issues. ... Yankees manager Joe Girardi said he plans on starting retiring 1B Mark Teixeira on Friday.