The Reds play at home competitively for the first time in the 2026-27 campaign when Nottingham Forest visit on Saturday lunchtime.
Van Dijk is hoping he and his teammates can showcase their improvement from the previous term and, more recently, last weekend's 2-2 draw away at Newcastle United.
In his column in the matchday programme, the captain writes: "It's great to be back at Anfield ready to attack another Premier League season, and I hope you guys are looking forward to Saturday's game as much as we are.
"Playing at this amazing stadium is a privilege we should never take for granted, and even as I begin what is my 10th season as a Liverpool player, I still get that same feeling. I can't wait to get out there.
"Last weekend's game up at Newcastle was a tough one. I think you saw a lot of good things from us, in terms of our performance levels, but also a lot of areas we need to improve in.
"That's normal. When you have a new coach with new plans and new ideas, it is always going to take a bit of time to put those into practice. But it is down to us to do that as quickly as we can.
"I can tell you that we are working extremely hard every day on the training ground, because we all want to improve, we want to be better and more consistent. We want to win, ultimately. At Liverpool, that should always be the aim.
"You don't need me to tell you that last season was tough, unacceptable in my opinion. We are better than that, much better in fact, and now we need to show it.