He showed guts and determination in the second round where he beat Chinese Lin Haifeng in sudden-death extra time after a 5-5 draw over three rounds.
Nacha, who also won the silver medal at last year's Asian Championship in Bangkok, continued his unbeaten run in the third round, where he thrashed Frenchman Belhadj Yassine 5-2.
It became even more thrilling in the last 16 when he beat Filipino Go Tshomlee in a hard-fought bout 12-10.
Nacha remained an impossible nut to crack in the quarter-finals and the semi-finals, where he beat Mexican Antonio Mata 6-4 and Brazilian Marcel Ferrier in sudden-death after a 3-3 draw.
Against Grgic in the final, Nacha took a commanding 4-2 lead in the first round before Grgic stormed back with aggressive kicks to level at 4-4 and then moved ahead to 6-4, sending the Thai to the floor twice with his powerful foot kick.
Nacha fought back gallantly in the final round, but the Croat was just too strong.
"It's a pity I could not make it," said a tearful Nacha. "I needed just one more point to get a chance to make amends. I felt pain in several parts of my body, but I just tried to get rid of it and fought it all-out here."
Despite the loss, Nacha will get an incentive of Bt500,000 from the Sports Authority of Thailand. His silver was the third for Thailand. Yaowapa Boorapolchai and Chatchawal Khaola-or clinched the first two silvers.
Meanwhile, team-mate lightweight Chonnapas Premwaew, the bronze medallist at the previous world meet in Madrid two years ago, failed to make her mark after crashing out in the round of 16 following a bitter 2-3 loss to Canadian Karine Sergerie.