Dublin-born O'Neill played junior football in Ireland for Bulfin United and was an Irish schoolboy international.

[3] He was spotted in a youth international match in Brentford by Everton and signed as a professional with the club in May 1949, the "Toffees" seeing him as a potential replacement for 39-year-old Ted Sagar.

O'Neill played in the 1953 FA Cup semi-final against Bolton Wanderers and shared the goalkeeping duties with Harry Leyland during the promotion campaign of 1953–54, as Cliff Britton led the club to a second-place finish, behind champions Leicester City on goal average but ahead of Blackburn Rovers by a single point.

[4] He remained though for further mid-table campaigns in 1958–59 and 1959–60, and played a total of 213 league and cup games during his time at Goodison Park.

However, in 1963–64 Waddington placed his faith in the new signings of Bobby Irvine and Lawrie Leslie and O'Neill, the eldest of the three, was now the third-choice keeper.

[1] He was preferred ahead of Ken Hancock and Reg Davies, and played 13 games of the 1964–65 season, as the "Valiants" were relegated out of the Third Division.

O'Neill won his first Republic of Ireland cap in a 6–0 defeat at the hands of Spain on 1 June 1952 in Madrid.

O'Neill was not a tall man, but he was an extremely acrobatic keeper with a natural ability to catch powerful airborne shots and make it look easy.