The Reds suffered the first defeat of Arne Slot's tenure as they were beaten 1-0 at home by their visitors, with Callum Hudson-Odoi scoring in the 72nd minute.
It was only Van Dijk's third defeat in 101 Premier League games at Anfield and it's something that he does not want to happen again.
'Everyone is coming back from different places and playing a different way, but still I think even though we weren't at our best we created chances and should have done better,' he said after the game.
'It's a performance we are definitely not happy with and we expect a lot better from ourselves. Losing at home is definitely something that can't happen, but we have to turn it around pretty quickly.'
Virgil van Dijk has admitted that his side's defeat by Nottingham Forest was unacceptable
The Dutchman added: 'In my opinion we have a very good group that really understand that today was unacceptable, disappointing, and we all know that everyone can do better, and the only way to show that is on Tuesday.
'That's what we'll focus on. We've been through losses and difficult moments together, and I think we have to stay calm and we will stay calm.
'We need the whole squad. We all know that after the international break it will be a game every three days, so we need everyone in the best shape and best form.'
Saturday's result leaves Liverpool three points behind Man City in second in the Premier League table, with Pep Guardiola's men having maintained their perfect start to the season with a 2-1 victory over Brentford.
Slot's side will be looking to return to winning ways when they face AC Milan away in the Champions League on Tuesday.