The loss followed Monday's 9-8 walkoff win to open the series in which they came back from being three runs down, as well as Sunday's come-from-behind 7-5 win against the Cubs when the Giants scored two runs in the ninth.
"We haven't felt like we've been out of a game in a long time," Belt said. "There's something special about this team that always feels like we're capable of winning the game."
The extra-inning affair saw the Giants match a Major League record by using 11 pitchers. Starter Ryan Vogelsong departed with one out in the fourth inning, with the bullpen combining for 7 2/3 innings of relief.
The Giants had a chance to take the lead in the bottom of the eighth when Hunter Pence got to third base with no outs and the score deadlocked at six runs apiece. But Joaquin Arias struck out, and after Xavier Nady walked, Hector Sanchez grounded into a rally-ending double play.
"We couldn't quite finish the deal in the eighth with the golden chance there where we couldn't get a run in," manager Bruce Bochy said. "But you have to like the way we fought back. We just couldn't quite finish it."
The final out in the bottom of the ninth initially looked to be heading toward the seats as a walk-off home run when Sandoval blasted a shot to the right-center-field wall, but the heavy San Francisco night air and the depth of the outfield in that corner combined to allow a running Justin Upton to make the catch before bumping into the wall to preserve the tie.
"That's a tough area. There isn't another ballpark that's that deep, so you know if it's hit out there, you have a shot at it," Upton said.
In yet another uncharacteristically shaky outing, Vogelsong allowed six earned runs in 3 1/3 innings, getting pulled after allowing a two-run blast to Aaron Hill that gave the D-backs a 6-2 lead. Vogelsong had been the National League ERA leader as recently as Aug. 12, but has now given up 24 earned runs in his last five starts (21 1/3 innings) to raise his ERA from 2.27 to 3.29.
"I thought he had good stuff," Bochy said. "The pitches might have caught up with him. He was working hard out there and his pitch count got up, and that might have taken a toll."
Belt helped key the comeback when he drilled an 0-2 pitch from D-backs starter Ian Kennedy into McCovey Cove for a two-run home run in the sixth inning to pull the Giants within 6-5.
"The guys did a good job swinging the bats," Bochy said. "The pitching has struggled a little bit here, but we're battling back, which is always a great sign."
The game followed Monday's 10-inning contest, and the Giants were able to hold on to their 4 1/2-game lead in the division standings after the Dodgers also dropped an 11-inning game to the Padres, 6-3.
"It's nerve-wracking, but it's been a lot of fun just to play in these games and see everybody working their butts off," Belt said of the extra-inning games. "It's not a lot of fun when we lose games like this, but having everybody doing their role has been a lot of fun to see."