Some politicians had previously raised concerns that members of the public and neighbours had seen the cull taken place and had heard gunfire in the area.
In the statement on Thursday, Muir said that there were no sounds of “loud gunfire” and that “silencers” were used.
The minister said efforts had been made to undertake the cull in parts of the fields which would “minimise exposure to public view”.
He added: “Although complete screening from all possible vantage points could not be guaranteed, efforts were made to keep the operation out of public view.”
The minister also outlined that a local farmer approached Daera staff at the scene to indicate a potential interest in purchasing some of the animals and that “operations were halted”.
He added: “The local farmer seeking to purchase some of the animals, another individual and the herd keeper were facilitated to remove the animals from a field into a lorry. They chased the animals for a significant period of time and released them onto a public road which created further health and safety risks.
“While those actions delayed the completion of operations, ultimately, Daera staff had to intervene as the individuals were unable to detain the animals which by that stage were stressed. At this time there was a small number of protesters at the site, but operations did not recommence until they had left the scene.”
The minister outlined that the remaining cattle were moved from the road and were “subsequently euthanised”.
Muir said it was a “complex and distressing case” for his staff and condemned threats and online abuse that had subsequently been made against Daera staff.
Earlier this week the minister ordered an external review into the incident and he is due to appear before a Stormont committee on Monday.
