Girardi expressed his feelings to The Athletic in his first interview since being dismissed as the Yankees' manager on Thursday.
The 53-year-old Girardi said his conversation with Brian Cashman was "fairly quick" when the general manager told him that he would not be returning to the club.
"Brian told me as an organization they had decided to go in a different direction," Girardi said. "We talked for a few minutes and we talked later on for a little bit longer. For me, there was disappointment because I kind of wanted to finish what we had started this year. And I was looking forward to the growth of the organization, the young players, the more young players with the veterans we had.
"I was very excited about 2018. But in a lot of respects, I'm really thankful. I was there for 10 years. How many managers, head coaches in the NFL, NBA, NHL, college football coaches, college basketball coaches, get to spend 10 years in one place?"
Girardi concluded a four-year, $16 million contract with the Yankees, who fell one win shy of advancing to the World Series this year -- losing Game 7 of the American League Championship Series to the Houston Astros.
After the Yankees lost in the ALCS, Girardi said he would once again discuss his situation with his wife and three children.
ESPN's Buster Olney, citing sources, said that Cashman recommended to owner Hal Steinbrenner that the team change managers.
Girardi took significant criticism for his team's loss in Game 2 of the ALDS versus the Cleveland Indians after failing to ask for a replay review on a strikeout that was incorrectly called a hit batsman.
Girardi managed the then-Florida Marlins for one year before taking over with the Yankees in 2008. He guided the club to the World Series title in 2009 and six playoff appearances.
Girardi owns a record of 910-710 with the Yankees. His win total ranks sixth in franchise history, trailing only Joe McCarthy (1,460), Joe Torre (1,173), Casey Stengel (1,149), Miller Huggins (1,067) and Ralph Houk (944).
As a catcher, Girardi played for 15 seasons with three World Series titles in four years as a member of the Yankees.