Baines netted a penalty this evening as Everton saw off the challenge of League One side Oldham in their fifth-round replay.
The 28-year-old is now hopeful of going further in the competition but Everton will have to beat Baines's former club Wigan in the next round.
The England international told ITV Sport afterwards: "We've been close [to reaching the final] a couple of times and that whets your appetite. We want to go further but we've got a tough tie next.
"We're at home so we'll be favourites, but we've had tough games against them the last couple of seasons and they're coming off the back of a good win at the weekend so they'll be confident."
The quarter-final at Goodison Park, which takes place at 12.45pm on Saturday, March 9, will be the first of the last-eight ties to be played.