I offered to quit, says boss Adams.
He said: 'I felt I had a moral obligation to say if they felt I wasn't the right man to take this club forward, I would step down.
Fortunately, they said I was the right man for the job.'
Adams also insisted his players were 'innocent until proven guilty'.
He criticised the players for boozing, but said he knew some of those arrested were 'not there' when the alleged incident took place.
Adams added: 'A minority of players let the club down but if they are guilty of anything it is of being unprofessional 24 hours before a training session of being drunk to excess.
'If I am guilty of anything, it's that I didn't put a curfew on the players. It has been a difficult time for me but I am not quitting.
'I owe it to the fans of Leicester City to see this through. The players, the last time I saw them, were shocked, horrified, scared.'
The six players released last week by the Spanish authorities returned to the training ground in Leicester yesterday for the first time.