Trent Alexander-Arnold jumped from the bench to hit the winner on the day.
Slot said afterwards: "I think we did (deserve it). We dominated definitely, which is also what you can expect if you go to Leicester. But I think you also have to give credit to Ruud van Nistelrooy, who just keeps trying to play in the best possible way and I saw a few very good moments from them also today.
"It is not a team that kicks every ball long, they try to play, they try to create. You can expect that we are the team that creates most chances and it is the first time since I am here that we have missed so many big chances because normally we are better in scoring one of them.
"Today, it was not a big chance that we scored – it was again a set-piece. Another big moment for us to score from a set-piece with us putting so much effort in for nine or 10 months now. It feels really good that in the moment we needed it most, although we needed it against Paris Saint-Germain as well when we headed it on the post from Jarell (Quansah). Now, two big moments for us to score from a set-piece."
Away fans have been sensational
Slot was particularly happy for the away support, who have followed Liverpool up and down the country this season in huge numbers.
Slot also said: "They definitely were (sensational). The only thing the fans want is us winning the league.
"They were involved, but not as much as they probably wanted. Every moment that it happens, it would be special for them. (I am) definitely looking forward to next week because I assume that Arsenal, because they are such a good team, are able to win during the week. We probably have to do it ourselves and the first chance we have is next week against Tottenham."
Liverpool can clinch the Premier League title this weekend against Tottenham and Slot expects his players to retain their focus during this coming week.
"I have to wait and see because I haven’t experienced it here yet but what I know from my time with Feyenoord is that of course there is a lot of noise and everybody is very excited, but at our training ground we are just focused on the training sessions we do and trying to prepare in the best possible way for Tottenham, which is a team where all the injuries are coming back and are a team that deserves our full attention.
"The boys also have one or two days off during this week because we’ve planned that already a long time ago and hopefully they will enjoy some time with their loved ones and be fully focused when we are back together to work towards Tottenham."