Despite what the Holland captain described as an “almost complete” performance in Sunday’s dismantling of West Ham, the Dutchman knows there will be more difficult hurdles to overcome.
Liverpool finished 25 points adrift in fourth place last season having drawn 12 matches.
Van Dijk said it was those kind of results they needed to eradicate.
“The most important thing is that we look at ourselves,” he said when asked about competing with City.
“We know that right now we have a great squad. We have a lot of quality players. Everyone who plays for Liverpool has a lot of quality.
“It’s all about being consistent. We want to challenge for any competition.
“Of course, we want to challenge. I do not feel any pressure in that case but we play every game to win, that’s how our mindset is.
“It’s just one game. We had a good pre-season with good results and games where we’ve played very well.
“But we can do a lot better and it’s just the start. I think the key is we need to be very consistent and do it every game.”
“I was not really worried to be fair,” added Van Dijk.
“I’ve played a couple of games pre-season with Joe at centre-back and I have a very good relationship with him, a very good understanding outside of the pitch as well.
“We need everyone in the squad. It’s very important at our club. Everyone needs to be ready when we need you. Everyone realises this.”