Van Dijk, 26, joined Liverpool in January in the hope of playing important matches on the European stage and the defender put in an accomplished display to keep out the likes of Gabriel Jesus and David De Bruyne.
Goals from Mohamed Salah, Alex Oxlade-Chamberlain and Sadio Mane secured a three-goal advantage over City at Anfield ahead of the second leg.
It was difficult to fall asleep, Van Dijk told Liverpools official website when asked about his emotions after the first-leg victory.
The game at home was an amazing example – everyone was 100 per cent focused and at it. Everyone showed their quality.
And you see what can happen. It was a total performance; in the first half we dominated possession and had our good moments and scored good goals; in the second half we defended as a unit and it was a fantastic game.
The Dutch centre-back warned his team-mates against complacency ahead of their trip to the Etihad.
You cant deny that being 3-0 up is going to be a little bit in your mind, he said.
But we need to go into the game with the mindset that its still 0-0. We want to win the game and we want to play well.
We know how good they are, we know their strengths and weaknesses as well.
We need to be ready for everything that is possible – and we will be.