Ginobili, 39, left Monday night's Game 4 with 2:25 remaining in the fourth quarter to a standing ovation from the San Antonio crowd and chants of "Manu! Manu!" and "One more year!"
The four-time NBA champion and two-time All-Star thanked fans for the gesture on his Twitter account Tuesday morning.
"Very hard to find the words to describe my feelings after yesterday's game. Still overwhelmed. Thank you SO very much!," Ginobili tweeted.
Ginobili said he has not yet made up his mind about retirement.
"I'm getting closer and closer (to the end of my playing career)," Ginobili told reporters after the game. "There is no secret, for sure. It's getting harder and harder. But I always said that I wanted to let it sink in for three weeks, four weeks, whatever, and then I will sit with my wife and see how it feels.
The Argentinean has spent his entire 15-year career with the Spurs, averaging 13.6 points on 44.7 percent shooting along with 3.6 rebounds, 3.9 assists and 1.4 steals in 992 career regular-season games.
This season, Ginobili averaged a career-low 7.5 points, 2.3 rebounds and 2.7 assists in 69 games.
"Whatever I decide to do, I'll be a happy camper," Ginobili said. "I have to choose between two wonderful and truly wonderful options. One is to keep playing in this league at this age, enjoying every day, playing the sport I still love. The other one is to stay at home, be a dad, travel more, enjoy my whole family."
Ginobili, who did not start a game during the regular season and has started only three times over the past five seasons, was in the starting lineup for Game 4 against the Warriors.
He finished with 15 points, seven assists and three steals in San Antonio's 129-115 loss.
"We started him tonight out of respect," Spurs coach Gregg Popovich said.
That was the whole reason for starting him. Before the game you think it may or may not be his last game that he ever plays in, and I did not want to miss the opportunity to honor him in front of our home fans for his selflessness over the years.
Ginobili averaged 13.8 points and 2.8 assists during the four-game series with Golden State, but just 6.6 points, 2.4 rebounds and 2.4 assists in 16 games this postseason.