The Reds booked their place in the fifth round on Saturday thanks to a 2-0 win at Championship side Bournemouth.
Jones now hopes that the Merseysiders can go all the way to Wembley Stadium and win the tournament for an eighth time.
"We've spoken about it and we want to try to get as far as we can - it's important for the club," he told the club's official website.
"We want to try to give the fans another day out at Wembley, if not two. This is how you progress, you've got to come to places like this and win. That was important."
Liverpool return to action on Tuesday night when they host local rivals Everton in the Premier League.