Johnson is now facing jail after being found guilty of sexual activity with a girl aged 15.
A statement on the Sunderland website following her resignation added: "In light of what has been acknowledged by Margaret as a serious error of judgment on her part, we have undertaken a full review of the club's decision-making processes to ensure that there can be no such mistakes in the future.
"Throughout this deeply regretful situation, we recognise that one devoted young fan and her family have been very badly let down, first and foremost by Mr Johnson and his despicable actions, but also by the club they support. We are so very sorry for this.
"Mr Johnson lied to the club; he also lied to our fans and they have every right to feel aggrieved by this. Lessons have been learned and we hope that the club and its fans can move forward from this together."
"Margaret (Byrne), in her role as CEO, was responsible for the running of the club. She was also accountable for the actions taken by the club in relation to Mr. Johnson.
"Sunderland AFC acknowledges that Margaret's intentions have always been to act in the best interests of the club, however it has become clear through our own internal investigations that in this instance decisions have been taken by Margaret in error.
"Whilst swift and decisive action was taken to terminate Mr. Johnson's employment upon his guilty plea, decisions taken prior to this, including the decision not to suspend him for a second time pending the outcome of the trial, were wrong."
In a statement, Margaret Byrne said: "I recognise that, as CEO, my involvement with Mr Johnson and the decision to allow him to continue to represent Sunderland was a serious mistake."