Morrissey came through the junior ranks at Anfield before signing professional forms in May 1957 shortly after his seventeenth birthday. Kevin Lewis blocked his way into the team on the right wing but he played regularly from 28 January onwards in the 1960/61 season. Roger Hunt's injury opened the door for him as outside-left Alan A' Court was moved to the middle giving Morrissey a run in the side on the left. With the up-and-coming Ian Callaghan on their books Morrissey was deemed surplus to requirements by Liverpool's board of directors that decided to sell him over Shankly' head for a give-away £10,000 in 1962. Bill threatened to quit over this matter and actually wrote a resignation letter. Morrissey, who was a tough customer and uncompromising on the field, played over 250 games in a successful spell for the Blues who won the League Championship in 1963 and the FA Cup three years later.

Morrissey earned the respect of the Anfield Iron, Tommy Smith, in their many battles on Merseyside. "You don’t expect wingers to be the bravest of the brave. However, there was one who you handled with care, simply because he was likely to get the first tackle in and the second one if you let him! His name was Johnny Morrissey and he played for our arch-rivals," Smith said. "He was fearless. The Everton fans called him “Mogsy”. He looked more like a boxer than a footballer."