The 15-year-old claimed the top amateur prize, the Smyth Salver, for the second straight major after finishing at nine-over.
With the last two rounds played on Sunday, Ko fired a four-over 76 in the morning followed by a six-over 78.
Jiyai Shin of South Korea avoided mistakes in miserable weather conditions to stroll to a nine-shot victory.
Shin held a three-shot lead after shooting a one-under 71 in the morning. She then stayed calm while strong winds and heavy showers sent scores soaring at Royal Liverpool in the afternoon, closing with a 73 to finish with a nine-under total of 279.
She was the only player to finish below par, with fellow South Korean golfer Inbee Park second on 288.
Shin's victory completed an Asian clean-sweep of this year's four women majors.
Koreans Yoo Sun-Young and Choi Na-Yeon won the Kraft Nabisco Championship and US Women's Open respectively, while Feng Shanshan became the first Chinese player to win one of the big four at the LPGA Championship.
