Dominik Szoboszlai's free-kick proved the matchwinner for Liverpool on the day.
Slot conceded afterwards: “We have nine points out of games where last season we picked up five points. So, that’s only positive but I do know and understand that we can do better.
"If we play this game 10 times more in the same fashion then I think it’s eight times a draw, we win it one time and Arsenal wins it one time because it was an uneventful game, which is something sometimes positive as well because both teams were really good in rest defence and in defending.
"But, I think normally Arsenal and us are able to create more chances during a game, but it tells you also something about the structure and the amount of discipline both teams have without the ball. Then you need a moment of magic, which we got from Dominik, and that resulted in us winning a game that, like I just said, normally would have ended in a draw. But I don’t agree with you on the first game, I think we totally deserved to win the Bournemouth game, by the way."
However, while he admits Liverpool aren't firing on all cylinders, Slot says he is delighted with the attitude his players are showing.
Asked what he's happy about after their first three games of the season, he replied: "Mentality. Having to bring quite a lot of new players in because quite a few left and then if you have to start the season against Bournemouth – who were last season already really good and this season again are already on six points – playing Newcastle away, which is for every single team in the league one of the most difficult away games, and then playing Arsenal at home, which is definitely one of the three or four most difficult games of the season.
"Then already doing what we are doing – we are not perfect and we were not perfect last season, by the way, as well.
"But still what you can see is a great mentality and everybody wants to work so hard to get a result over the line and then you need a little bit of luck, which we had at Newcastle (and) today.
"But, I’ve said this so many times, I think it was Michael Jordan (who said), ‘The harder we work, the more luck we get,’ and that is something I think you can say about this team. They work incredibly hard and there will be moments in the season where we work just as hard and we don’t find the luck of scoring a goal, but we always give ourselves a chance because we work so hard."