Chief Executive Carrie Lam had said she was highly disappointed that more than a dozen senior officials were among the 180 or so people at the banquet last Monday, and she was particularly disappointed in Tsui.
One of the guests at the event later tested positive for coronavirus.
On his Facebook page, Tsui said he had not put enough thought into how to respond to the party invite.
“Recalling what happened now, officials are not ordinary citizens, we should set higher standards for ourselves than for ordinary people,” Tsui wrote.
“I should have been more cautious and turned down the invite, when it was the most critical moment to fight the pandemic.”
Tsui said he is very sorry for not living up to people’s trust and expectations, and he is willing to bear the consequences and make up for his mistakes.
He added that he can’t change what happened, but he will learn from it and won’t commit the same mistake again.
The minister said he has spent time during his quarantine at Penny’s Bay reading and vetting documents.
Meanwhile, Tsui’s deputy Jack Chan said he has returned to work after he was told he could end his isolation.
In a statement issued through the government, Chan apologised for also accepting the party invite, saying he will learn from his mistake and be more cautious in future.