The chief executive of the US Anti-Doping Agency, Travis Tygart, has responded emphatically to claims made in a document released by the UCI on Monday, saying that cycling's governing body are "simply diverting attention away from their own failures".

On Monday, the UCI president, Pat McQuaid, convened a press conference to deliver the UCI's verdict on the Usada report, published two weeks ago, which had revealed the extent of the doping scheme that enabled Lance Armstrong to win seven consecutive Tours de France. The report's publication followed Armstrong's decision not to contest Usada's case against him in an arbitration hearing – even though that decision meant he would be stripped of all his titles.

In Geneva, McQuaid said the UCI recognised the Usada ruling and that Lance Armstrong now "had no place in cycling". But in a document published later the same day on the UCI's website, and personally signed by McQuaid, he delivered a different message. The UCI's "Decision" document accepts Usada's sanction against Armstrong, but calls its evidence and methods into question, and raises grounds for a possible appeal – either by Armstrong himself, or by the World Anti-Doping Agency – against the report's conclusions.

After first welcoming the UCI's announcement on Monday, Usada's Tygart reacted indignantly on Tuesday, once he had reviewed McQuaid's critique. "The truth is Lance Armstrong, on their watch, pulled off the greatest heist sport has ever seen," said Tygart. "Instead of attempting to explain or justify their inadequacies, the UCI should acknowledge their responsibility and failures and find ways to make it right."

During the press conference McQuaid had to field uncomfortable questions over the UCI's acceptance of $125,000 in donations from Armstrong. In the four-page "Decision" document, however, McQuaid refers to the Usada report's "overstated language", "incorrect and incomplete statements", and questions whether Usada had a sufficient "degree of detachment" to make a disciplinary judgment.

"The UCI does not point to any specifics in making this ridiculous claim," responded Tygart, via email from Usada's Colorado headquarters, after reviewing the document. "They simply are trying to divert attention away from their own failures in this whole sad saga, and those that love the sport of cycling and clean sport should not allow that to happen.

"Our report was straightforward and produced the natural and logical conclusion based on a simple review of the evidence," he continued. "Maybe they do not like the outcome but it is the simple sad truth, nothing more and nothing less and their effort to undercut is obviously a transparent attempt to continue to run from the truth."

In the document, McQuaid also challenged the jurisdiction of Usada in stripping Armstrong of his titles under the Wada Anti-Doping Code and publishing its report after Armstrong waived his right to a court of arbitration for sport (Cas) hearing. McQuaid suggested that Armstrong "could have contested not only the allegations that Usada made against him but also the jurisdiction of Usada". According to McQuaid, the UCI should have been given Usada's case file for the UCI to decide on what action to pursue.

"We set forth our position on why they were conflicted in this case on many different grounds," said Tygart, "They accepted money from him [Armstrong], they accused us of a witch-hunt (without seeing any evidence), they sued the chief whistleblower, they discouraged witnesses from participating."

In the UCI "Decision", McQuaid claimed that if his body had had prior sight of Usada's evidence, it would have concluded that Armstrong "had a case to answer" and would have advised Armstrong's national governing body, USA Cycling, to institute proceedings. Tygart has little confidence that an investigation led and controlled by the UCI would have produced the same result.

"All in all, given what was at stake for the sport," said Tygart, "I was very doubtful this day would ever come".

Perhaps the most serious of McQuaid's claims is that Usada deprived Armstrong of the benefit of an eight-year statute of limitations under Wada's Code. Theoretically, this would rule out of court all Usada's evidence of doping violations prior to 2004, the year of Armstrong's penultimate Tour de France victory. McQuaid goes on to note that this statute of limitations could have formed the basis for a partial defence if Armstrong had accepted a Cas hearing on his case. The UCI president adds that while the UCI itself would not appeal to Cas on the basis of this claimed infringement of the statute, Wada should, or could, in his view, make such an appeal for the sake of enforcing compliance. In short, the UCI advises Wada that it has a responsibility to appeal against Usada's ruling against Armstrong's doping operation.

"Armstrong denied himself the benefit of any statute because he lied under oath and many other forums, swearing that he did not dope, in addition to bullying witnesses into silence," Tygart responded. "If he had not done this, he might have benefited from the statute of limitation. To raise this now, only further shows their reluctance to do the right thing for the sport going forward."

Tygart added that he would have been happy to have seen the case go to Cas, rather than be settled by Armstrong's waiving of his right. "We welcomed a Cas proceeding for all the evidence to be presented under oath and in public for the world to see, and we were confident the world would know the truth, as it does today."

In a section in the "Decision" commenting on Usada's evidence, McQuaid casts several aspersions. Implying duress, he notes that witness statements "have been under penalty of perjury" and "have not been submitted to cross-examination".

"Even if, purely as an assumption," noted McQuaid, "some statements made against Mr Armstrong would be incorrect, vague or confusing, the UCI does not have the elements to show that this would be the case."

"[This is] another example of the UCI attempting to escape responsibility for their failures and it is quite sad they would continue to resort to such underhanded tactics at this time," said Tygart. "This is absolutely fiction, made up by them to justify their ineptness at failing to prevent this 'great heist' in their sport."

McQuaid closed the UCI document with the proviso that the UCI's recognition of the Usada ruling is conditional "on whether Mr Armstrong or Wada will appeal Usada's decision to Cas". Given the history of tension between the UCI and Wada – McQuaid and his predecessor Hein Verbruggen even sued Wada's former head, Dick Pound, over his criticism of their anti-doping efforts – an appeal by Wada seems very unlikely.

According to Jay K Reisinger, a Pittsburgh-based sports law attorney, Armstrong would have 21 days to lodge an appeal – notwithstanding the fact he declined a hearing. As Usada's "Reasoned Decision" was published on 10 October, that would give the disgraced cyclist until the end of the month.

Despite what might be seen as the encouragement offered by McQuaid to Armstrong in the UCI document, Tygart is not losing any sleep over a move by Armstrong himself. "Armstrong has waived his right to any appeal," he said. "He does not have any right to appeal at this time."

Tyler Hamilton, Armstrong's former team-mate and self-confessed doper, believes McQuaid should now step down. "Pat McQuaid's comments expose the hypocrisy of this leadership and demonstrate why he is incapable of any meaningful change," said Hamilton. "Instead of seizing the opportunity to instil hope for the next generation of cyclists, he continues to point fingers, shift blame and attack those who speak out. Tactics that are no longer effective. Pat McQuaid has no place in cycling."