"What happened last year definitely helped our drive and helped us stay focused for an extended period of time," he said. "It very easily could have hit us in different ways and we could have reacted in different ways.
"But we reacted the right way. We got great leadership from the top in (coach Gregg Popovich) who came back absolutely fired up and ready to go. To push us this far and this hard and to come out with the championship is amazing."
The Spurs routed the two-time defending champion Heat 104-87 on Sunday to win their fifth title and first since 2007.
San Antonio Spurs and Miami Heat split the first two games of the series but something changed for the Spurs and they were virtually flawless in the next three games to claim the title.
Last year, the Spurs, leading 3-2 in the best-of-seven series, squandered a five-point lead in the final 28 seconds of regulation of Game Six and lost 103-100 in overtime.
San Antonio then lost Game Seven and spent the offseason wondering how the game slipped away.
There were missed foul shots in that painful sixth game, missed open jumpers and missed defensive assignments.
On Sunday, the Heat raced out to a 22-6 lead and the once-boisterous San Antonio crowd of nearly 19,000 turned quiet, wondering if another meltdown was in the cards.
"We knew they'd come out with energy," the 38-year-old Duncan said of the Heat.
"We knew they'd come out and try to knock us down early, and I think we helped that. We just came out, we weren't getting shots up, we were turning the ball over.
"We were doing exactly what we did when we lost Game Two (98-96). But we kept our focus. We kept saying to each other that it's a long game and it's going to turn."
The Spurs battled back, outscored the Heat 25-11 in the second quarter and led 47-40 at halftime.
Eight minutes into the third quarter, San Antonio had a 65-44 lead and the game was all but over.
Manu Ginobili, who scored 19 points on Sunday, also said last year's disappointment was instrumental in winning this year.
"Last year was a tough one for all of us," he said. "We felt like we had the trophy, that we were touching it, and it slipped away. It was a tough summer. We all felt guilty.
"We all felt that we let (our) teammates down. But we worked hard. Every game in the regular season we were trying to get better, to have the same opportunity again. We got to this spot, and we didn't let it go.
"As you could see, every game we were up 15, 20, we kept it. No mistakes. Great mentality, and we kept playing until the last minute."