Under current Australian laws, all international arrivals are required to be vaccinated against Covid-19 unless they have a medical exemption.
Djokovic said he was under the impression he could enter because two independent panels associated with Tennis Australia and the Victorian state government had granted him an exemption because he had been infected with Covid-19 in December.
The federal government argued that, under its rules, previous infection with Covid-19 is not a valid reason for an exemption.
The Australian Open started on Monday but the tournament's media day on Saturday was dominated by
players being asked about Djokovic.
"As the Australian tennis family, we recognize that recent events have been a significant distraction for everyone, and we deeply regret the impact this had on all players," added the Tennis Australia statement.
"There are always lessons to learn, and we will review all aspects of our preparation and implementation to inform our planning -- as we do every year. That process always starts once the Australian Open champions have lifted their trophies."
Had Djokovic played and won this year's Australian Open, he would have secured a record 21st men's singles grand slam title.
"We, like the players, and all tennis fans here and around the world, are keen for the focus to now be on the game we are all so passionate about," continued the Tennis Australian statement. "We are looking forward to a brilliant two weeks of tennis ahead."
The Australian Open ends on January 31.