The ABC revealed Senator Thorpe had not disclosed she was in a relationship with former Rebels president Dean Martin while serving on the parliamentary law enforcement committee.
The committee had been receiving confidential briefings about bikie gangs at the time.
Greens leader Adam Bandt requested Senator Thorpe's resignation from the party leadership in the wake of the revelations, which she accepted.
He said her failure to disclose the relationship was a "significant lack of judgment".
"As leader I expect my senators and MPs, especially those in leadership positions, to exercise good judgment," he said on Thursday.
"At a minimum, Senator Thorpe needed to disclose to me her connection to Mr Martin and her failure to do so showed a significant lack of judgment."
Senator Thorpe said she had accepted the mistakes she had made.
"I ... have not exercised good judgment," she said in a statement.
"I will now reflect on this and focus on my important portfolio work, especially advocating for First Nations people."
Mr Bandt said he was not aware of the revelations about Senator Thorpe's relationship until he was contacted by the media.
He said it was disappointing the relationship was not disclosed.
"People are entitled to trust that where there are issues that affect the work of senators, all members of parliament, that they will be disclosed," he said.
"It is disappointing because it is an error, a significant error of judgment from someone who has a lot to offer this country and a lot to offer this parliament."
Mr Bandt said the senator had not been involved in the justice portfolio since the May federal election.
