After the Austrian champions fought back to restore parity at Anfield on Wednesday night, Mohamed Salah then fired home in the 69th minute to get the Reds off and running in Group E.
Although Jürgen Klopp's side are reigning holders of Europe's premier club competition, Van Dijk welcomed the fact improvements can still be made.
The centre-half told Liverpoolfc.com: "Our mentality is that you just keep going no matter what happens.
"If there is a goal conceded or we score a goal, we want to keep doing what we are doing. We want to keep going.
"We conceded three goals at home, obviously that is not a good sign, but that's maybe a good thing that we still have to improve - and we will. I think there is no reason for panic.
Watch: Liverpool 4-3 Salzburg in 90 seconds
"When we conceded the first goal in the first half they kept believing. Obviously, they would never give up anyway, even if they were 4-0 down. We knew that.
"But the goal we conceded in the first half gave them a little bit more hope to go into the second half. And the second half, especially the first 20 minutes, they did well and we didn't. They were clinical with the chances they had.
"But still we should have done better. Maybe it is a good thing that we still have to improve a lot - and we will."
Van Dijk stressed Liverpool will carefully scrutinise the goals conceded and look to correct any errors ahead of Saturday's Premier League meeting with third-placed Leicester City.
He added: "You see that Salzburg is a very good team. They play a little bit similar to us I think - a lot of pressing, a lot of energy. They don't want teams to play through them and they have great players as well. We respected that.
"Maybe we should have done better in certain moments. We will analyse that and hopefully do better at the weekend."