"We wear in-ear monitors so we can hear ourselves when we're singing at games, and last night mine failed during the song I sang before the game.
"We switched them over before the anthem, hoping that would fix the problem, but when I got out there to sing they started crackling pretty severely before they cut out entirely."
She said she couldn't hear anything and lost her place in the anthem.
She removed the ear monitors and was able to carry on, but said she felt "utterly devastated".
"Gave it everything I had to finish it off, but I felt like I'd let everyone down, and there were a few tears after."
She said event organises believed the cause of the disruption was a "frequency issue", and she had been overwhelmed by messages of support since the anthem.
"I am so very sorry. But sometimes these things happen, unfortunately, so I'm dusting myself off and moving forward."
Marvelly also took to Twitter to apologise, saying sorry to "New Zealand, and especially the NZ Maori".
All Black Jerome Kaino sent her a message back, saying "You were Amazing Lizzie!!!".
It's not the first time this year technical issues have had an impact on the presentation of a rugby game.
Sky Sport host Andrew Mulligan had difficulty pronouncing words during a live halftime interview with Stormers player Robert du Preez.
He joked that he was "Drunk AF" on Twitter afterwards, before revealing the real cause to be feedback coming back to him through his earpiece.