McQuaid had described Hamilton and Floyd Landis, who also testified against Armstrong, as "scumbags" on Monday after the UCI ratified the US Anti-Doping Agency's decision to strip Armstrong of his seven Tour de France titles.
Hamilton and Landis were among the 11 former Armstrong team mates to testify against him.
"Pat McQuaid's comments expose the hypocrisy of his leadership and demonstrate why he is incapable of any meaningful change," Hamilton wrote in a statement on Tuesday.
"Instead of seizing an 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."
McQuaid had started to thank those who had testified before the USADA but then directed his anger at Hamilton and Landis, the first Armstrong team mates to break the code of silence.
"Landis started it, he was in a bottomless hole and he said the only way out of it was to bring the sport down," McQuaid said on Monday after his hour-long media conference in Geneva.
"Another thing that annoys me is that Landis and Hamilton are being made out to be heroes. They are as far from heroes as night and day. They are not heroes, they are scumbags. All they have done is damage the sport."
Both Landis and Hamilton have said the UCI covered up an Armstrong positive test for the banned blood booster EPO at the 2001 Tour de Suisse.
The UCI, however, have denied covering up a test, producing on Monday what they said was evidence that an Armstrong sample was 'suspicious', not 'positive'.
"We did not cover up anything because there was nothing to be covered up," said McQuaid.
Landis, who was stripped of his 2006 Tour title for doping, admitted in 2010 to using performance-enhancing drugs and said his former team leader at US Postal, Armstrong, also cheated.
- Sports & Recreation
- Floyd Landis
- Pat McQuaid