The Reds came from 1-0 down to win at Anfield, with Mohamed Salah hitting the winner.
Slot said: "We needed another second-half performance but because we were outplayed in the first half. They were better on the ball, more aggressive without the ball. Then, everything changed in the second half because it was completely the opposite.
"Our attackers scored the goals but the main difference was we were better positioned and we had the ball a lot more. Without the ball they made problems for us but in the second half we just kept running."
On going top of the Premier League, he added: "It's more if you play against Arsenal in their stadium and you can get a draw away from home. Brighton are a very strong team as well, they have shown this season. If you face a team like this and are 1-0 down and can come back to a 2-1 win which in my opinion was deserved that gives me a lot of confidence. More than the position we are in."