Roberto Firmino began and ended the scoring, with goals from Sadio Mane and Adam Lallana in between, while Lucas Leiva's mistake briefly gave the Foxes hope when Jamie Vardy made it 2-1 just before half-time.
Ranieri conceded his team were second best.
"Liverpool played better than us and deserved to win," he said.
"We were waiting for this kind of football. First match at home (for Liverpool), new stand and I think we started well but after the first goal we lost our counter and they played so well.
"We wanted to do something but Liverpool won the first ball, the second ball, they were inspired tonight.
"Everything they tried to do was okay and it was difficult for us."