"If you had asked me before heading to Miami I would have said okay, I'll take it. Winning one and losing the other by 20, not a big deal. I'll take it," he said.
"But once you win the first one, you forget about that. Odds are over and you face a new game as if it's a Game Seven and you want to win it, too. Knowing full well that they were going to come hard, they were going to play a better game.
"But we were expecting to do better, that's the frustrating part," he added.
Miami went on a 33-5 run in the second half as the Spurs failed to get to grips with the Heat offense and struggled to convert their own chances.
Ginobili said Miami's comprehensive win would infuse them with confidence.
"Sure if you look at the result, 1-1, it's not bad. But you don't want to play like this in an NBA Finals," he said. "You don't want to give them that much confidence, and you don't want to be feeling bad about yourself.
"In the second half they just ran us over. We didn't move the ball at all. Their pressure really got us on our heels."
San Antonio's 'Big Three' of Ginobili, Tony Parker and Tim Duncan combined for just 10 of 33, with only 27 points between them.
The Argentine said that had to change. Quickly.
"For sure Tim, Tony and me, we have to step up and play much better," he added. "We have basically no shot at winning a game against them if none of us play good."
Game Three is on Tuesday in San Antonio, the first of three games scheduled for Texas.
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