The 2-0 win ends a run of four consecutive Premier League defeats, with Mohamed Salah and Ryan Gravenberch scoring on the night.
Slot said afterwards: "Happy with the result, with the performance and what I saw today, not only from the players but also the support we got from the fans, was what we needed today. Maybe we were a bit more on the lucky side than we've been in the last few weeks, where in my opinion we were also unlucky.
"So, the mistake of their goalkeeper and the deflection led to two of our goals. These are the margins we are talking about. I think in other games we've created more from open play than we did today. But in football it's about results, not about the chances you create from open play.
"A lot of course, especially because it happened at 0-0 and not when we were leading and not when we are top of the league. When you are in a difficult situation as a club, as a team, and because I'm definitely part of that – it is also a difficult situation for me – and then to get the support the players got but also that I got, that is something what makes this club special.
"They don't forget if you've been part of something special and they help you, especially if things are difficult. That's what it was in the last few weeks, things were difficult. We were not winning, we were losing and they felt the players and maybe even me needed a bit of support – and that's what you get then from these fans."
Slot was particularly pleased with how the team controlled the tempo of the game on the night.
He explained, "Like in Frankfurt – and the comparison between these two is that we were leading. In other games, we've mainly after five minutes been 1-0 down and then you get a completely different game. Now I think everybody liked it, the way we controlled the game in the end and how we were passing and playing through them.
"Where if you do the same and you are 3-1 down and it doesn't lead to a chance or a goal, people get a bit annoyed that you don't create a chance. So, you cannot compare a game of football where you are 2-0 up to a game of football where you are 3-1 down when it comes to control. This is, I think, what we prefer to see – being 2-0 up and having a bit more control. If we need goals then we need to be more open and as a result of that you sometimes see a counter-attack as well."