Mr Nulty, who quit Labour to sit as an Independent in protest at austerity measures, said he was standing down as a TD after admitting sending inappropriate Facebook messages to a 17-year-old girl.
Minister for Social Protection Joan Burton said she was “shocked and very distressed” when she heard the revelations regarding her constituency colleague.
“I certainly just found it utterly unacceptable and I would be very concerned for the people who had what must have been a very difficult experience for them.
“No person should have to put up with that sort of stuff,” said the Social Protection Minister.
Referring to one of the explanations Mr Nulty offered for his behaviour, Ms Burton said: “I know that he said he has issues around alcohol and I hope he’s able to deal with those issues.”
Communications Minister Pat Rabbitte said Mr Nulty had no option but to stand down due to the “sad affair”.
Mr Nulty has gone to ground since the Sunday World revealed the story.
Though it has been reported that the 17-year-old’s mother has contacted the gardaí regarding the matter, a spokesperson for the source said no official complaint regarding Mr Nulty’s actions had been received.
In one of the messages, Mr Nulty asked the teenager: “Have you ever been spanked?”
In his resignation letter, Mr Nulty referred to the 17-year-old, who he believes he has never met, as a “woman”.
Further allegations that he may have sent inappropriate messages to friends of the 17-year-old have also been reported.
The Sunday World revelations that prompted Mr Nulty’s resignation included allegations he asked a female constituent to post underwear to him, and another to wear a skirt when visiting his office.
The resignation means the Dublin West seat will see a second by-election this Dáil, the first coming as a result of the death of Brian Lenihan. One bookmaker placed the Socialist Party’s Ruth Coppinger as favourite to succeed in the four-seater.
However, Fianna Fáil is to mount a strong challenge after its candidate David McGuinness came second to Mr Nulty in October 2011.
Neither Mr Nulty, nor his staff, were available for comment.
While the Oireachtas monitors the activities of Dáil and Seanad staff using its computers, it cannot overlook the online activities of any public representatives or their political staff because of confidentiality and privacy issues.
But TDs and Senators have been issued with a code of practice or Acceptable Usage Policy which was announced in June 2012.
It says members, and their staff, should not use the internet: for any unlawful purpose; to visit sites that contain obscene, pornographic, sexist, racist or any other objectionable material.
Neither should they use it for the purpose of commercial gain or profit, or to download any software from the internet.
It says use of Oireachtas internet services “must be appropriate to the performance of members’ duties as elected representatives.”