Mohamed Salah's spotkick gave the Reds the lead before VAR overturned a second penalty call for Curtis Jones just before halftime. Moises Caicedo found an equaliser for Chelsea three minutes after the break, but Jones struck on 51 minutes for Liverpool, which eventually proved the winner.
Slot later said: "Yeah, of course (I am pleased) with the outcome. Because if you win then you're always pleased about the outcome. In an ideal world we would've outplayed them completely. That's definitely not what we did. It was an equal game, in my opinion. There were phases in the game where we had to work really hard not to concede, but it's very pleasing to see that is also what we did.
"I think we all saw the great block tackles Dominik (Szoboszlai) and Curtis had - Curtis first half, Dominik second half. Those moments are just as crucial as the goals we scored and added to that, there were a lot of eventful decisions by the referee, which made it the game it was. I think if you're not a Liverpool supporter or Chelsea supporter, you really liked what you saw today. In the end, also if you are a Liverpool supporter you liked what you saw today.
"I think it was mostly the media that told us that this was our first big test. I think if you go to Old Trafford against a very strong team like (Manchester) United, that is definitely a test as well. I said, I think it was Friday in the press conference, don't judge us on this week, you have to judge us after six, seven or eight (more) games. That's also what I say now after this win because Wednesday is Leipzig, Sunday it's Arsenal, then it's Brighton, Brighton (and) then it's Leverkusen and Aston Villa.
"So, this is in my opinion our biggest test, to play Champions League and Premier League; the hardest games three days in a row. That's what (Manchester) City did last season, that's what Arsenal did - both of these clubs did this for two years in a row now. You saw two years ago how difficult that was for us and you saw last season how difficult it was for (Manchester) United and Newcastle to be involved in the Champions League and Premier League. That is for me the test we have to go through to see if we can stay or be where we are now."
On Jones, Slot added: "I think what we all made of this today. He had a very good game. He had a difficult job to control Cole Palmer, which is an incredible player, in my opinion. It's so difficult to defend him because he has so many qualities. Curtis did that really well today.
"In my opinion, he controlled him for most parts of the game; it's almost impossible to control a player like this for 90 minutes, but he was quite close to that. And then to even have an impact on the other side with a goal and two penalties that he was involved in, one of them was in the end disallowed by the VAR, but that shows you that he had a big impact on both sides of the pitch."