The Reds open their campaign in today's Third Round tie against Accrington Stanley.
Van Dijk wrote in his match programme notes: "The FA Cup is a competition which means a lot to both players and supporters.
“I personally have great memories of it. We have won it before and we would like to go as far as we can in it this season as well.
“In my opinion, one of the big strengths of English football is the quality of teams lower down the league pyramid. The Premier League takes most of the attention, but the standard of football in the Championship, and in Leagues One and Two, is very good also.
“You see that in the FA Cup, a tournament which is famous for its giant-killing stories down the years. Many top teams have come undone against supposed lesser sides, and we need to be fully focused to ensure our name is not added to that list on Saturday.
“I can assure you all that that will be the case. The mentality of this squad is very good, and is one of the big reasons we have started this season so well. We cannot, and will not, allow complacency to creep in now. Accrington Stanley deserve our full respect, and that is exactly what they will get.
“We are all looking forward to the game, and I am sure you all are too. It was amazing to see nearly 6,000 of you guys down at Tottenham, and I know you will give us amazing support once more as we attack another competition.
“It never goes unnoticed, I can assure you.”