The south coast club defeated local rivals Portsmouth 2-1 on Saturday to progress to the fifth round of the Cup. They will now face Everton at Vitality Stadium in the next round.
Regarding Bournemouth's rise to prominence over the past few seasons, Elphick spoke about now gaining a foothold in the prestigious cup competition with a sustained run in a bid to create more history.
He said: "We've done some extraordinary things over the last three years with the core players of the group having remained from League One. Going from strength to strength.
"Re-writing history? It's hard to take stock. The minute you do that you might lose out.
"You can't take anything for granted. We know how fragile the game can be and have to keep working hard every day to do better.
"We are still putting ourselves on the map and hopefully a Cup run like this will do that. We can make out mark on the competition."