Alexis Mac Allister headed home the game's only goal in the second half of the well-earned win as Slot's men handed the LaLiga leaders their first defeat this season in Europe's elite competition.
“Impressive because we played against an incredible side, a team that's on an unbelievable run of form, only lost once, won all their other games," Slot said. "If you then can win against them and perform how we have, that's very positive,” Slot said.
“It’s been (some) tricky weeks for us, many away games, hardly any rest in between every single game. It helps if you can play in front of these fans and you can play in front of Real Madrid because I think that brings the best out of my players and out of our fans.
"A great performance ... It could have been a bit more maybe."
The Dutchman also praised his side’s defensive discipline, especially in keeping Kylian Mbappe and Vinicius Junior quiet.
"I said before the game that they have scored 26 goals in LaLiga, and Mbappe and Vinicius together have 24 goal contributions," Slot said. "So, if you want to win this game you have to make sure that these two are not on the scoresheet."
Slot singled out 22-year-old right back Conor Bradley for his standout performance.
“Conor was outstanding. To be up against Vinicius so many times one v one is not for everyone. He did outstanding today,” Slot said.
The victory was Liverpool's second in a row after their 2-0 Premier League win over Aston Villa on Saturday ended a dreadful run of four consecutive league losses, and six in seven games across all competitions.
"We had a very bad run of form in terms of results. No excuse in the world can make up for us losing so many games," Slot said. "But we had to play a lot of games in a small amount of time. Tonight, we played against a team that played on Saturday as well, so the both of us had two days rest.
"And it's helpful to play in a home game, because from the last eight, I think we played six away from home. So the fans can give you just a little bit of an extra edge if you are maybe a little bit tired."