The Premier League leaders were rarely tested as Cody Gakpo and Mohamed Salah struck for the hosts.
Slot said afterwards: "At the end the result is the most important but the performance was great. If you want to win against a team like City you have to be good at every part of football. So high defending, low defending, build-up, high, low, everything. Because they bring so many challenges to you.
"I think we weren't perfect but we came quite close to managing it all.
"In every game you want to start in the best possible way, but we did start the way we wanted it. That always helps because if you start poorly the fans are against you. If you start like this it gives energy to the players. They see the game plan is ok for them, so they created chances like this. And also with the crowd behind you that also gives you extra energy."
Asked if Liverpool waste chances, Slot continued: "That's true. Although I watched this game every time when I was not working here so maybe this game deserved the way it went because it was special until the end. But if you only look at it from a Liverpool perspective, it would not have been strange if we were two goals up at half-time or any other point of the game.
"City were dominating possession but still the chances were for us.
"You have 90 minutes of concern when you play City because they can cause you troubles or problems in every single second of the game. Even if you are 2-0 up you think like this. I saw a game with my former club doing something special. But no, you never feel comfortable when you play City because of the quality of their players and their manager."
On staying calm as leaders, he added: "That's what I'm trying. During the games these managers bring you a lot of problems in the Premier League, they're all great managers. And the players that play here make it difficult as well. So you have to be calm and collected and see what happens.
"You just try to prepare your team in the best possible way and not get too carried away with a win or a loss."