Armstrong told Britain's Daily Mail that Verbruggen insisted "we've got to come up with something" to explain the American's positive tests for a banned corticosteroid.
A backdated prescription for a saddle sores cream was accepted, allowing Armstrong to continue racing and win his first Tour.
"His story is illogical because it was not about a positive/punishable act according to the anti-doping authority involved," wrote Verbruggen, adding that cycling's governing body did not have lead responsibility for anti-doping at the race 14 years ago.
"That authority was not the UCI but the French ministry. From accusations a year ago about large-scale complicity of the UCI in doping by Lance Armstrong and his team, we're now back to a cortisone case from 1999 that was not even handled by the UCI," said the former president, who stepped down in 2005 after Armstrong's seventh straight Tour victory.
Verbruggen, the honorary UCI president and an honorary IOC member, is a likely witness for an independent commission panel which the UCI is creating to investigate claims of collusion to protect Armstrong from scrutiny.
The UCI and World Anti-Doping Agency said in Johannesburg last week that the panel could begin work early next year.
Armstrong is expected to be the star witness and has suggested he wants a reduction in his lifetime ban imposed last year by the U.S. Anti-Doping Agency.