He also apologised for "degrading language" used about her in a Whatsapp group with friends after the incident.
Jackson, 26, and fellow Ireland international Stuart Olding, 25, were found not guilty of raping the woman in Jackson's home in the early hours of June 28, 2016.
But the eight-week trial has led to widespread criticism of their behaviour towards women and calls for them to be permanently dropped from the Ireland team.
In a statement released to the Press Association news agency, Jackson said he was "ashamed that a young woman who was a visitor to my home left in a distressed state."
"That was never my intention and I will always regret the events of that evening," the statement said.
He also apologised unreservedly for engaging in a Whatsapp group chat which was "degrading and offensive."
"The criticism of my behaviour is fully justified and I know I have betrayed the values of my family and those of the wider public."
The language in the statement was significantly more self-critical than a statement by his lawyer after the trial which focused on the "heavy price personally, professionally and financially" suffered by Jackson and his family.
In the trial Jackson was also acquitted of a separate charge of sexual assault. Two other men who faced charges in connection with the incident were also found not guilty.
Neither of the players, who between them have represented their country 29 times, have played for their club, Ulster, or at national level, since they were charged last July.
The Belfast Telegraph newspaper on Friday published a letter from "concerned fans" calling for Olding and Jackson to be permanently dropped from the Irish team.
Jackson's decision to sue an Irish senator who criticised his behaviour on twitter sparked a wave of criticism online and helped fuel street protests calling for changes to Irish law on rape.
A lawyer for Jackson, Joe McVeigh, did not immediately respond to a request for comment.
(Reporting by Amanda Ferguson and Conor Humphries; Editing by Toby Davis)
