In his first season, he beat Richy McDonald, Steve Lemmens and Karl Broughton en route to the last 128 of the 1994 European Open, but lost at this stage 0–5 to Wayne Brown.

In the 1997 World Championship, he won three matches - beating Karl Beare 5–2, Jason Pegram 5–4, and Joe Grech 10–5, to reach the last 128, but lost there 1–10 to Nick Dyson.

Starting the 1999-2000 season ranked 132, Abernethy continued where he had left off, beating Dene O'Kane and Prince again to reach the last 64 of the 1999 British Open, but there he lost 4–5 to James Wattana.

His best performance of the season came in the same event as in the previous, the 2000 Thailand Masters; this time, he overcame Troy Shaw, Matthew Couch, Jonathan Birch, and Brian Morgan to qualify again for the last 32, but could not progress any further, losing 2–5 to Ken Doherty.

He began the following season ranked 81, but could not improve upon this performance, only equalling it in beating Sean Storey and Patrick Wallace before losing in the last 64 of the 2006 China Open to Wattana.