The champions took the lead with just over a minute to go in their 101-100 defeat against the Mavericks, whom they knocked out of the playoffs last season.
The shooting guard told reporters: "It's special. I think it helps you actually. Sometimes you don't play that sharp because it's the first game of the season.
"You have to move from the success of the previous season to the new beginning. But it all gets your emotions up so you want to get out on the court and do a lot of things, hustle, jump, run and win."
The Spurs are in action again on Friday against the Phoenix Suns.