Forest thumped the defending champions 3-0 at Anfield, leaving Liverpool in the bottom half of the table with six defeats already this season.
Asked if he is confident there is a "way out" for him and his players, Slot replied: "Of course there is a way out, especially with the quality players we have. I think no matter if you win or you lose, if you make a line-up and if you make substitutions and when you look back you're always thinking about, 'Where can we do better? Where can we adjust?' But that's something else than doubting yourself.
"I want to emphasise one more time on the fact that I'm responsible for the current losses. You are responsible when you're winning, but you're also responsible when you are losing. Although you asked me that question, not to talk about referee decisions or other excuses, I can never come up with enough excuses to have the results we have. That is far from good enough and I'm responsible for that."
Slot also insisted: "It is my responsibility. If we win or lose, it is my responsibility. But what I also see is the team and, by the way, our fans as well stay until the end, support the team until the end and the players keep on trying until the end.
"What I also saw today, but it wasn't at City - and at City we are not the only team that struggles in the first half - and in every other game we've played, we've been the dominant team and we were able to create chances."
The Dutchman added, "I see a lot of things where in a normal situation the result would have been different, but we are now in a difficult situation and then you need to do even more to get your results than when things go in your favour."