The Reds reached their first European semi-final for 10 years after securing an emphatic 5-1 aggregate win over the Premier League champions.
Karius admits that the two victories over Pep Guardiola's side brought the players closer together and spurred them on to dream of "something special" in the competition.
"Especially after we beat Manchester City quite impressively we thought: 'Wow, we've done really good and we can reach something special here,'" Karius told Sky Sports News.
"I think those two games meant a lot and brought us closer together, with the way we played and with the fans as well in the first game, how amazing they were.
"We're a great group, you can see that I think. Everyone is working for each other."
Liverpool went on to beat Roma in the semi-finals to book a place in the final against Real Madrid in Kiev.