Cormier triumphed over Johnson by making him submit to the rear-naked choke with more than two minutes remaining in the third round.
Despite tapping out, Johnson made it clear that there are no hard feelings between him and Cormier.
He added that Cormier had backed up everything he said prior to the fight.
"He did everything I thought he was going to do," Johnson said after the bout. "He did everything I thought he was going to do.
"I have no excuses for why I lost. He was just the better man. I have nothing but respect."
Johnson also pointed out that the loss will not stop him from achieving his goal of becoming the UFC's light heavyweight champion.
"Tonight I might have lost, but the one thing I want you guys to remember is that you should never give up," he said. "I was pushed down to the bottom and I worked my way up to the top. I want you all to know no matter what comes your way in life, never give up."