Darwin Nunez and Mohamed Salah struck for the Reds' 2-0 win.
Slot later said, "It wasn't easy like most of our games have been now. Aston Villa were maybe not as aggressive as we thought they would be. We were patient. One thing they are very good at is set-pieces. In general we had control over the game and scored from two counter-attacks which is maybe not what we would expect.
"The set-pieces are for someone else. It is not the first time Liverpool score from breaks like that because we have players who are so fast."
On Nunez's goal, he said: "I wondered what would happen if he wasn't there because Mo was through on goal. Darwin was there and he scored and that's good for him. With players around him who score so many goals it's always good as a striker to get on the scoresheet."
"We are really happy that most of our players have stayed fit through this tough run. We have to wait and see how Trent is doing. If I look at the games that are ahead they are tough. It will be a tough season in general. Margins are small, we have a margin but it is small. Many challenges to come for us."
On Salah, he added: "I think he has the best numbers from all our attackers. All our attackers have great numbers but Mo stands out in that aspect."