Sangakkara was just eight runs short of a double-century when he was struck on the shoulder by a bouncer from paceman Stuart Clark.
The ball ricocheted off his helmet to Australian captain Ricky Ponting at second slip, who appealed for the catch, and Koertzen raised his finger to end Sangakkara's innings on 192.
Television replays showed that Sangakkara should not have been given out and Sri Lankan skipper Mahela Jayawardene later revealed that Koertzen had apologised to him.
"Rudi came and said sorry to him," Jayawardene told a news conference after Sri Lanka's 96 run loss gave the hosts a 2-0 series sweep.
"Kumar being Kumar was fine with it. He was very disappointed at the particular moment but when you sit back after half an hour, you know it's a mistake made by a human and that's it."
Ponting said he appealed for the catch because he heard two noises so assumed the ball had brushed either Sangakkara's gloves or bat.
"I think we all reacted on the two noises we heard at the time," Ponting said.
"It sounded like it was either glove or bat and up into his helmet.
"As we all know things happen pretty quickly on the field especially when there's a bouncer being bowled to a batsman like that.
"I obviously caught the catch and appealed and went up for it and he was given out."
Sangakkara's 192 was the highest score by a Sri Lankan in a Test against Australia.
He batted more than seven hours and struck 27 boundaries and a six in a brave attempt to salvage a draw for his team.