The former Leinster and New South Wales Waratahs coach added while he did not agree with the decision to appoint Johnson, he had felt he could get the team to perform well enough to clinch their third World Cup title in Japan.
“I loved Australian rugby and I thought I could do it, I believed I could get the players together and I didn't want to let the players and the supporters down,” Cheika said.
“I tried to manage it the best way I could without being out of order.
“If you cause turbulence at that point, everyone feels it and I didn't need everyone to feel the turbulence in the team.
“You have to deal with it internally.”
Cheika, however, ended his tenure as coach with a parting shot at RA management, saying he had virtually no relationship with then CEO Raelene Castle and Chairman Cameron Clyne, who have both since stepped down.