The government has begun an inquiry into the events of last Sunday, in conjunction with the country's police.
World football's governing body Fifa is also investigating.
The LFA believe the deaths were caused mainly by suffocation at one of the ground's crowded gates at the Samuel K Doe Stadium.
The secretary general of the LFA, George Williams, admitted his association were responsible, but said the situation could have been much worse.
"Generally, we know we had a situation where there were more people at the game than the stadium could cater for," he said.
"The repercussions were that there was overcrowding at a particular gate and that then led to suffocation, which is unfortunate."
"We had fire trucks that were there to spill water over the crowd and that really helped the overall situation.
This should be a wake up call for everybody to ensure that we don't have a repeat of where we are going to endanger our spectators
Kalusha Bwalya
"Them spraying water over the people reduced the level of suffocation and also helped the crowd calm down.
"Yes, we (the LFA) are responsible, but things could have been worse.
"At the moment, we know that eight people have been killed. There are injuries as well, but these are not that significant."
Meanwhile the president of the Football Association of Zambian, Kalusha Bwalya, has told BBC Sport that the tragedy in Liberia should be a warning to the rest of the continent.
The former African Fooballer of the Year also recently inspected safety and security at the main stadium in Sierra Leone on behalf of football's world governing body Fifa.
"In terms of the ongoing qualifiers this should be a wake-up call for everybody to ensure that we don't have a repeat of where we are going to endanger our spectators," he said.
"Eighty per cent lies with the associations in Africa - so that we provide the necessary security and the necessary rules and regulations so people without tickets don't go to the stadium.
"Twenty per cent lies with the supporters themselves - so that they won't want to come to the stadium without a ticket and thereby causing a problem."
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