Ms Keay had argued she took all the steps she could to renounce her British citizenship but she had accepted the High Court decision.
"This is not a valedictory speech, let me be very clear", she said.
The High Court ruling could also spark a by-election in the Adelaide Hills seat of Mayo, where the Nick Xenophon Team candidate Rebekha Sharkie defeated former Liberal minister Jamie Briggs.
Labor leader Bill Shorten has been accused of "lying" to the Australian people over the dual citizenship fiasco.
Lamb said she meant to recontest her seat and Labor MPs Josh Wilson and Justine Keay, who also resigned on Wednesday, and independent member Rebekha Sharkie, said they would do likewise in their separate electorates.
Labor already faces a byelection for the seat of Perth, with Tim Hammond announcing last week he would resign for family reasons.
He said he was pleased that the Labor dual citizens would run for re-election, although he was not sure if one of them, Susan Lamb, was still a dual national.
Dates for the by-elections have not been set officially but could be as early as mid-June.
The Labor line on the decision is that "the law has changed".
"Here they have done so by establishing how the law operates in the context of someone in Katy Gallagher's position".
Labor leader Bill Shorten said three of the ousted MPs would seek re-election.
Neither side looks forward to a plethora of byelections, which are expensive and with unpredictable fallout, so close to a general election.
Gallagher has always maintained she took all reasonable steps to renounce her British citizenship by the nomination deadline before the 2016 election. This did not apply with United Kingdom citizenship. "The big message here for anyone who might want to be a member of parliament in the future is to renounce now".
Porter rejected her argument that her circumstances were different.
While the MPs can recontest their seats to re-enter parliament within two months - as several other MPs have done - Gallagher will be replaced by her Senate running-mate, forcing her to wait until the next election to re-enter parliament.
The citizenship crisis has claimed nine federal parliamentarians since the election.
The procedure to renounce British citizenship was simple and the requirements not onerous.