Ko sided with Thompson, saying that the viewers should not be able to alert officials to potential penalties.
Tiger Woods was also amongst the many top golfers who disagreed with the decision.
The penalty dropped Thompson back into the pack chasing the title, and through tears she battled back, giving herself an eagle putt on the last for victory. It came up an inch short, and she went to a playoff against So Yeon Ryu.
There, Ryu made a birdie on the first playoff hole to seal her second major title, and deny Thompson an emotional victory.
Ko had a far less dramatic day, shooting a two-under 70 to complete a solid four days, bouncing back from missing her second career cut the week before.
Ko only shot four bogies throughout the tournament, but never managed a low round to come close to defending her title.
The 11th-place finish is Ko's 14th top 25 finish in her 23 career majors.
World number two Ariya Jutanugarn could have taken over at the top of the world rankings with a victory, but finished in a share of ninth place, and was surpassed in the rankings by Ryu.
Ryu now ranks a career-high second in the world, while Ko extends her run at the top to 76 consecutive weeks.
On the PGA Tour, Danny Lee shot an even-par final round to drop 10 shots, finishing in a share of 20th. Russell Henley won the tournament to book a trip to the Masters, which will have a field with no New Zealanders for the sixth time in seven years.