Rayan Ait-Nouri canceled out Ibrahima Konate's opener for Liverpool before Mohamed Salah converted a penalty won by Diogo Jota for the 2-1 win.
Slot later said: "I don't think we started well, but we have to give credit to Wolves and Gary O'Neil.
"They had a real good game-plan. We had some problems in the first 20 minutes, but afterwards we took control of the game.
"They overloaded our right side a lot with many players.
"Normally we try to press with Salah a bit more forward, but sometimes it is not about tactics, it is about how aggressive you press.
"How strong you are in the duels and in the second half we come out better - the energy and intensity was much higher.
"Sometimes we feel we have to be more patient against a low block team, I am not saying Wolves were that.
"We were patient and kept circulating the ball and kept waiting for the right moment to bring the ball in."
On Konate thinking he should be the player of the match, Slot responded: "Konate? Then maybe he forgot the moment we conceded a goal.
"That was the reason we conceded as he wasn't there and it was avoidable."
On being title contenders, Slot added: "I always try to be be realistic and Jurgen's work has been incredible everybody knows this.
"Two years ago was the last time they played in the Champions League and they finished fifth.
"Now we have to prove that we can compete in the Champions League and the Premier League."