USADA, in response, accused the UCI of "attempting to undermine and question the substance of our case."
The 40-year-old Armstrong was stripped of his record seven Tour de France wins last month and handed a lifetime ban by USADA after indicating he would not challenge charges that he had doped throughout his career. He has always denied doping.
UCI must ratify the sanction and USADA said on Wednesday the file case and reasoned decision will be sent to the UCI and the World Anti-Doping Agency by Oct. 15.
USADA boss Travis Tygart had said earlier that he expected the report to be sent by the end of the month.
"The UCI had no reason to assume that a full case file did not exist but USADA's continued failure to produce the decision is now a cause for concern," Pat McQuaid, the president of cycling's governing body, said in a statement on Thursday.
"It is over a month since USADA sanctioned Lance Armstrong. We thought that USADA were better prepared before initiating these proceedings," he added.
McQuaid had previously said he had no intention of contesting USADA's decision, unless the UCI was given serious reasons to do so.
The UCI noted in its statement that reports were suggesting USADA was still gathering evidence and has yet to complete its case file.
"It seems that it would have been more useful for USADA to have used the time of the Tour de France, the Olympic Games and the Road World Championships to prepare their case in full rather than to make announcements," the UCI said.
"It is at very least unusual that USADA would still be gathering evidence against a person after it has found that person guilty.
"The UCI assumes that the reasons for any difficulty in putting the evidence together will be explained in USADA's decision."
The world cycling body also criticised USADA for not having informed it directly about the delays.
"The UCI... has learnt of the reported delays through the media and not by any official communication from USADA," it said.
"The sooner the UCI receives the decision and case file the sooner the UCI can provide its response."
USADA's Tygart denied his agency had not been in touch with UCI.
"It is also troubling that they would claim to have had no contact with us which is inaccurate," the USADA chief executive said in a statement to Reuters.
"As they know we will be providing them the 'reasoned decision' no later than October 15 through the process and at that time the questions contained in their publicly released statement today will be answered."