After an early scare, Liverpool hit all three goals inside the opening 37 minutes via Luis Diaz (2) and Darwin Nunez.
"I think it was a good performance, especially with the ball," said Slot. "Quite a lot of shots on goal, a lot of chances, but not as easy as the score probably looks.
"They were really good finishes but it's also important what led to the finish. They were really aggressive, Bournemouth, so (Ibrahima) Konate understood a ball in behind was a good one to take. For the second Trent (Alexander-Arnold) made a good run with the ball and Luis finished both off really well."
On Nunez, he continued: "We hope we are adding goals because that is what you need from a striker but this work rate was really good. We have a lot of good players, a lot of competition, and as long as they keep performing it is a very good thing for me."
On Trent Alexander-Arnold's performance, he added: "I'm not surprised he is involved in so many goals because his quality is outstanding but what I also liked today was how he defended. If he can combine those two things he makes me really happy."
"It is normal we win a home game against Bournemouth but it is a tough schedule, and the teams you face are really strong. They made it a hard fight for us so it is good for us to win again and now let's continue."