Klopp wants Liverpool to remain positive in three-way title race
Brighton took the lead after just 84 seconds through Danny Welbeck but Liverpool stayed positive and goals from Luis Diaz and Mohamed Salah earned them the three points.
Liverpool have now won seven league games this season after conceding first, and Klopp said his side have come a long way in developing their collective mental strength.
"When I talk about being nervous as a whole unit, we were more nervous years ago," the German told reporters on Sunday.
"That's long ago but it is something we had to develop together ... If we all together enjoy this, then we have a chance. If we don't, we still have a chance, it's just really more difficult and that's why we try to stay positive in all these moments."
Liverpool, who face bottom side Sheffield United on Thursday, lead the league with 67 points, two points ahead of Arsenal and three ahead of holders Manchester City.
"We are there with two other teams fighting for the biggest prize in English football and we will see how it will end up," said Klopp, who is stepping down at the end of the season.
"But I decided I will try hard to enjoy it."