The double defending champion was locked in a battle of wills with Djokovic over five thrilling sets before suffering his first loss at the tournament since being beaten by Stefanos Tsitsipas in the fourth round in 2023.
"It was a very important slam for me, of course, (but) it can happen," the 24-year-old Italian told reporters.
"It was a good match from both of us. I had many chances. Couldn't use them, and that's the outcome. Yeah, it hurts, for sure."
Sinner had beaten Djokovic in each of their previous five meetings, but was not surprised by the quality of the tennis the 38-year-old Serbian was able to produce on Rod Laver Arena.
"He's won 24 Grand Slams," Sinner said. "We know each other very well, how we play. I'm never surprised by (his level) because I feel like he's been the greatest player for many, many years.
"Of course, he's playing fewer tournaments because of his age and everything, but we also know how important Grand Slams are for me, for him... and everyone.
"He played great tennis. Hopefully, I can take away some kind of a lesson to see what I can improve on."
Sinner held eight break points in the deciding set, but Djokovic saved them all.
"He came up with some great shots," said Sinner. "Most of the time, he served very well; you also have to say that. I had my chances. I was in the rallies a couple of times.
"I missed the shots, and it can happen. That's tennis, and that's how tennis works.
"But you have to give him a lot of credit for how he played today."
Djokovic will play Sinner's great rival Carlos Alcaraz in Sunday's final as he looks to secure his 25th major title and become the most successful Grand Slam tennis player, man or woman, of all time.