Armstrong was banned for life and stripped of his seven Tour de France titles by the International Cycling Union in October after USADA found that he had taken performance enhancing drugs throughout his career.
The USADA report into Armstrong's doping also alleged that the UCI had not done everything in their power to catch the former rider, who later admitted to cheating.
The UCI pledged to look into the past and set up an independent commission to investigate the allegations, only to disband it weeks later in favour of a broader "truth and reconciliation process" that has yet to start.
Speaking before a French Senate committee investigating doping on Thursday, Tygart, the man behind Armstrong's fall, repeated the accusations and said that the UCI was trying to "play a stall game".
In reply to Tygart, the UCI said on Friday that USADA and World Anti-Doping Agency were also to blame for the dismantling of the independent commission.
"It's all very well Mr Tygart talking about cooperation, but let's not forget that the Independent Commission was only disbanded because of USADA's and WADA's point-blank refusal to cooperate with it," the UCI said in a statement.
"Simply, the UCI was left with no choice but to close it down; it made no sense to go forward without the participation of these two bodies."
The Swiss-based body also suggested others had been to blame for the failure to catch Armstrong sooner.
"One can only assume that their refusal to cooperate with the Independent Commission was due to their fear that their own shortcomings would be exposed," the statement said.
"After all, USADA and WADA also tested Armstrong over many years and also failed to catch him. It was only with the benefit of the US Federal Investigation that USADA was finally able to gain evidence of Armstrong's doping."
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