He has always denied taking performance-enhancing drugs but chose not to fight Usada's charges against him.
The UCI has been criticised
for failing to do more to prevent doping. However, McQuaid, who took over from Hein Verbruggen in 2005, said he had "no intention" of resigning.
"This is a crisis, the biggest crisis cycling has ever faced," said Irishman McQuaid. "I like to look at this crisis as an opportunity for our sport and everyone involved in it to realise it is in danger and to work together to go forward.
"Cycling has a future. This is not the first time cycling has reached a crossroads or that it has had to begin anew.
"When I took over in 2005 I made the fight against doping my priority. I acknowledged cycling had a culture of doping. Cycling has come a long way. This is a landmark day.
"I'm sorry that we couldn't catch every damn one of them red-handed and throw them out of the sport at the time."
released a 1,000-page report
this month which included sworn testimony from 26 people, including 15 riders with knowledge of the US Postal Service Team and the doping activities of its members.
Usada praised the "courage" shown by the riders in coming forward and breaking the sport's "code of silence".
Armstrong, who retired in 2005 but returned in 2009 before retiring again two years later, has not commented on the details of Usada's report. His lawyer, Tim Herman, described it as a
"one-sided hatchet job".
McQuaid said he was "sickened" by what he read in the Usada report, singling out the testimony of Armstrong's former team-mate David Zabriskie.
"The story he told of how he was coerced and to some extent forced into doping is just mind-boggling," he said. "It is very difficult to accept and understand that that went on."
How does blood doping work?
Referring to the fact that Armstrong was tested for doping more than 200 times and never caught, he said: "The cheats were better than the scientists and we can't be blamed for that; we're a sporting organisation.
"But cycling has changed a lot since then. What was available to the UCI then was much more limited compared to what is available now. If we had then what we have now, this sort of thing would not have gone on."
Usada chief executive Travis Tygart welcomed the UCI's decision, but called for a new body to be set up to probe further into cycling's murky past.
"It is essential that an independent and meaningful Truth and Reconciliation Commission be established so that the sport can fully unshackle itself from the past," he said.
"There are many more details of doping that are hidden, many more doping doctors, and corrupt team directors and the omerta [code of silence] has not yet been fully broken."
McQuaid was quizzed over a $100,000 (£62,300) donation made by Armstrong to the UCI in 2002, a year after he had a suspicious test for banned substance eythropoietin
at the 2001 Tour of Switzerland.
Asked by BBC sports editor David Bond how he could justify the payment, McQuaid said: "We used the money against doping; it was done openly and put to good use."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.