Liverpool threw away a two-goal lead at West Brom on Saturday after goals from Jake Livermore and Salomon Rondon inside the final 11 minutes earned the Premier League's bottom side a point.
Van Dijk was disappointed with the draw at The Hawthorns, but believes the result is not a reason to worry ahead of Tuesday's first leg against Roma at Anfield.
“You have to tell each other the truth, you cannot be nice and happy when we want to achieve so much as a team and a club," said Van Dijk.
"A draw is not good enough but there is no reason to panic. There is no need to stress.”
Both West Brom goals came from set-pieces, something Liverpool have often been criticised for failing to defend this season, but the January arrival of Van Dijk had seemed to alleviate that problem.
He added: “I don’t worry at all. They [West Brom] are fighting for their lives so in the end they are very direct, balls into the channel, work hard, trying to get fouls and free-kicks and we didn’t cope with that how we should have.
“To concede two goals from set-pieces as well, where we have always the same roles to do and we didn’t do that. So, it is disappointing, but I am not worried at all.”
Roma are dangerous from set-pieces, scoring 20% of their goals this season from corners or free-kicks, including Kostas Manolas’ late header against Barcelona which set up the semi-final tie against Liverpool.
When asked about the potential danger of Roma’s set-plays, Van Dijk said: “They have set-pieces as well. They don’t play only set-pieces. Their boys play sometimes on the ground and then you can play football.”
A huge worry for the Reds will be Roma’s top scorer Edin Dzeko, who has scored 20 times in all competitions this season and he will be a danger from dead-ball situations.
“I have not played against Dzeko before but everyone knows the result against Barcelona," said Van Dijk. "They are a very good team and we have to be ready.
“I don’t fear anyone. We play a different style to Roma. It will be a different game to this one. The system we played at the end today won’t be the same."