The Wallabies were thrashed 54-34 in their Rugby Championship opener in Sydney last weekend, with only a late revival once the All Blacks had already run riot salvaging any pride.
Australia legend Lynagh tore into their performance on Sky Sports, saying their skills were "non-existent".
Cheika's side have the opportunity for revenge in Dunedin this weekend in the second Bledisloe Cup Test.
The Wallabies coach said there is little they can do to alter Lynagh's opinion aside from showing an improvement on the pitch.
"Where's he? Over in England isn't he?" Cheika said. "If that's how he feels, [we] can't change it except for what we do on the field.
"There's nothing else I can say to it, really."
Skills coach Mick Byrne, who formerly worked for New Zealand, took the criticism on the chin.
"When you're talking about a dropped pass or a missed tackle they're skillsets and yeah, they weren't up to scratch," said Byrne.
"When you're out there as a group working on changing habits, there is a period of time when sometimes it's not acceptable. I understand that.
"I honestly believe that when you're inside, we know where we are going with it. We are not executing some of the things we'd like to but we are trying to get better every day.
"When you look at the game and from a scoreboard point of view, some of the errors we made, we took some great learnings."