The Reds won 1-0 thanks to Diogo Jota's early goal, though also lost goalkeeper Alisson to injury.
Van Dijk said: "It is hard to come here. The results over the years are tight and close.
"I think obviously we scored a fantastic goal. We could have done better in the second half, but we knew they'd come out with a bit of pressure on the ball.
"It ends our run on a high before the internationals."
On having the best defensive record in the Premier League this season, he added: "We keep going and we keep working. We are never satisfied. We needed Alli twice, but that is what we try to avoid. Everyone is contributing to clean sheets.
"I think there is always expectations towards different teams - whatever the outside world thinks of us we don't really care.
"We want to try challenge, compete, win and be successful."