The 24-year-old reportedly struggled with nerves throughout this week's competition, failing to really find his form at an aquatics centre named in his honour.
The 2008 Olympic 400 metre champion's failure to land a gold at these Games has contributed to a disappointing outing for South Korea in the pool.
The host nation have failed to top the podium in a swimming event at the Asian Games for the first time since 1978.
However, after finishing fourth in the 1,500m freestyle earlier in the day, Park claimed his historic bronze in the 4x100m medley relay - a race won by China.
And China proved dominant on the final day of action in the pool - picking up three further golds, including a third win for double Olympic champion Ye Shiwen in the women's 200m individual medley.
China have surged clear at the top of the overall medals table and they had more to shout about in the weightlifting, as Zhou Lulu lifted the largest single weight ever by a woman to claim victory in the over-75 kilograms category - breaking the clean and jerk world record with 192kg.
Yang Zhe also triumphed for China in the men's 105kg, while the remaining gold went to Behdad Salimikordasiabi of Iran in the men's over-105kg.
Four of the six shooting golds on offer on Thursday also went in China's favour, and they completed one-twos in both the men's and women's trampoline contests.
South Korea wrestled back second place in the medals table from Japan, with two equestrian golds and a bowling win aiding their cause.
Elsewhere, Pakistan triumphed in the women's cricket competition with victory over Bangladesh, and Japan claimed gold in the mixed triathlon.