Armstrong was more critical of Cookson, who succeeded Pat McQuaid as president of cycling's world governing body in late 2013.
He said "everybody thinks" Astana should have been stripped of their World Tour licence after five positive doping cases relating to their team last year. But even if Cookson's hands were tied, which the Briton says they were due to a precedent set at the Court of Arbitration for Sport, Armstrong says he should have done more to force Astana manager Alexandre Vinokourov, Tinkoff-Saxo's Bjarne Riis and others to cooperate with cycling's independent reform commission [CIRC], which is shortly to deliver its report into cycling's doping culture.
Armstrong himself has spoken to the three-man panel twice and is hoping the commission recommends a reduction in his lifetime ban.
"If McQuaid had made the same decisions Cookson has made in his first year, he would have been lynched," Armstrong said, citing the Astana case and Team Sky's fast-tracked request for corticosteroids to treat Froome's chest infection at the Tour of Romandy. "Do we like what we have got so far?"
"If I'm Brian Cookson, I would make it a deal point that you have to come in and talk," he added of testifying to the CIRC. "So if Riis doesn't talk to you, or Vinokourov doesn't, there should be consequences. I don't know those to be examples, but I can imagine.
"If you don't come in to talk, you don't just get passed."