The severe weather event tore through northeast NT on March 17, bringing heavy wind and rain and cutting off communities.
An evacuation of the remote community of Borroloola on March 18 was called off after Australian Defence Force planes could not land as the eye of the cyclone neared.
Northern Land Council chair Matthew Ryan said the government response was inadequate and put residents in danger.
"Imagine being out there stranded, surrounded by rising water, not getting any clear direction, and seeing planes circle but then just leave," Mr Ryan said in a statement.
"The federal and NT governments' emergency response support has been appalling ... lessons are not being learned and as a result our communities continue to suffer."
The land council said staff met with federal government officials on March 12, warning them of the ongoing telecommunications issues and black holes accompanying severe weather events in remote areas.
The issues were noted, though when Cyclone Megan hit the week after, the council says communication was poor.
Several official emergency notices posted to Facebook diverted people seeking information to as many as eight different numbers or websites, the council said.
Future updates promised to be posted at specific times also did not eventuate.
Senator Malarndirri McCarthy says she will follow up on why a cyclone shelter had not been finished. (HANDOUT/AUSTRALIAN DEFENCE FORCE)
Residents said they had to wait in the wind and rain for evacuations, with an elderly person reportedly having a fit.
"We were hungry, we only had only apples, waiting there (on Monday) until 4pm ... they didn't come until Wednesday," resident Elton Daniels said.
"My brother Vincent Charlie had a fit waiting for the bus through that rain and wind ... having all those old people stand like that, it was very sad.
Hundreds of Borroloola residents were eventually evacuated to Darwin three days later, as floodwaters continued rising after the storm filled the MacArthur River.
But the residents say they felt let down and the evacuation was too little too late.
"For three nights I was sleeping with no power ... there was eight of us sleeping in that room, hungry because no shops open," evacuated resident Iris Hogan said.
"My granddaughter and this other girl, they were carrying me on (to the plane) and I was shaking, my bones, it was just terrible ... I cried in the plane."
NT Mining Minister Mark Monaghan told reporters on Tuesday that there was a "very fine window" to carry out cyclone evacuations.
"The bottom line of it is, if no one dies in these spaces how can you say it was a horror," he said.
"We made sure that they were fed (and) the kids had opportunities to be educated while away from their community."
Senator Malarndirri McCarthy told ABC Radio residents from her hometown of Borroloola were left traumatised by the incident.
"I know that Telstra is trying to do its best, but it really is not good enough that in times of crises that we've not been able to have thorough communication and this has caused further anxiety and stress," she said.
Senator McCarthy said she would be following up with the NT government on why the Borroloola cyclone shelter had not been finished on time.
