Ms Byrne said in a statement: "Contrary to what has been suggested, I did not understand that Mr Johnson intended to change his plea at trial or at all.
"I was astounded when he did plead guilty.
"I accept that Mr Johnson should not have been permitted to play again, irrespective of what he was going to plead.
"It was a serious error of judgement and I accept full responsibility for this."
A Sunderland statement read: "The Board of Sunderland AFC has today accepted the resignation of Margaret Byrne.
"Margaret, 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 light of what has been acknowledged by Margaret as a serious error of judgement 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."
It also emerged during the trial that Byrne did not inform manager Sam Allardyce about Johnson's admissions.
Allardyce was appointed in October and was told by the club that Johnson intended to protest his innocence, hence he continued to play him right up until February 6. The footballer earned £3million during this time.
However, Johnson pleaded guilty to kissing and grooming the girl on February 10 and was sacked by Sunderland the following day.
Allardyce said after the trial he did not know of the documents Byrne had in her possession.
Byrne had come under increasing pressure to hand in her resignation after Johnson's conviction last week.
Shadow sports minister Clive Efford said on Sunday: 'Sunderland have got some questions to answer.
"In employment law you don't have to have beyond any shadow of a doubt, you can take reasonable action.
"If there were concerns, they should have held up the suspension (he was suspended on March 2 for two weeks after his initial arrest) and not reinstated him.
"I think it's quite clear, in terms of safeguarding young children, I would say the club had no choice but to act and not restore him to the team.
"Sunderland were in possession of enough evidence to seriously question whether they were being told the truth.
"Their judgement, at best, is left wanting here. They should be giving clear answers to this to draw a line under this."
