The Dutchman was speaking ahead of today's Community Shield clash with Crystal Palace.
“You’re going into the season with goals that you want to compete for every trophy that you participate in. I think that’s the bare minimum for a club like Liverpool,” Van Dijk told liverpoolfc.com.
“Obviously it’s going to be very tough but we’ve been through very tough times anyway and I’m really looking forward to it. I’m looking forward to every bit of it.
“We’re all in this together and that’s how it should be. Us as a group with players, staff but together with our fans, we have to go together into this and support each other and be there for each other in the good and lesser-good days.”
It's about a legacy
The captain continued: “Any success with Liverpool, obviously that feeling is incredible. Last year we celebrated all together. That feeling when we were crowned champions against Spurs… they call it dopamine. It’s just incredible.
“Personally, I think that’s what you play football for. You want to be leaving a legacy behind, you want to be remembered, you want to inspire the next generation in everything you do.
“We are at a club where legends will be remembered and honoured and always be welcomed back. It’s an amazing feeling and an amazing feeling that we were part of that period of time, but we still are part of the club and want to be successful.
“It’s just amazing, it’s just a special feeling. Personally, I could have never dreamed about this when I was younger. That’s the beauty of football as well and the beauty of life: keep going, consistency, never give up and enjoy the whole ride that’s ahead of you.”