Winger Luis Diaz scored twice in three first-half minutes and Darwin Nunez netted his first league goal of the season to leave Bournemouth reeling, and they never recovered as Liverpool coasted through the second half to victory.
"(It was) not as easy as the score might show. I think Bournemouth were in the game, despite the fact that they were 3-0 down, they just kept on going, kept on going to the end, you don't see that a lot," Slot told broadcaster Viasat.
"I liked a lot the way we started the game, we were really aggressive, we created enough chances already before we scored the 1-0, and we kept defending really strongly until the end, which was necessary," he added.
After a toothless display against Forest, Slot was pleased with how his side implemented his game plan.
"Especially the way we build up from the back, the amount of times we were able to find a free player in the midfield - in the second half it happened a lot, but in the first half it led to chances," the 46-year-old explained.
Having taken over from Juergen Klopp in the summer, Slot's Liverpool are still a work in progress as he seeks to embed his playing style.
"That's why we're working on the training ground, to get the best out of the team, and as a result of that also from the individuals - they have to understand that everyone is related to each other," Slot said.
