Jurgen Klopp said he was "really pleased" that Liverpool could end a run of four matches without victory against league leaders Leicester City on Saturday
First-half substitute Christian Benteke scored the only goal just after the hour to inflict the Foxes' first loss in three months and first away from home since March.
Liverpool also prevented Leicester from scoring for the first time since May.
"It was deserved," Klopp said after the game. "We played too complicated at Watford last week [in a 3-0 defeat]. Today we did much better.
"We knew if we stayed concentrated we would get our chances as it was not too intensive in the first half so we could do more in the second half.
"We made this one goal but after all the set-plays of Leicester it was difficult and close and not easy to defend but we did it, we had patience and that is good so we deserved the three points.
"A lot of teams tried it before and it is not too easy so I am really pleased with what we did today."
The only blot on the day was another hamstring injury, this time to striker Divock Origi, who was preferred to £32.5 million summer signing Benteke from the start.
"Origi did really well. I hope it is not too serious, we will see," said Klopp. "Hamstring is the s--- word of the year for me. It is always hamstring, hamstring, hamstring -- that is the intensity of the game and fixtures.
"Benteke did really well in the last week in training but we decided on this starting line-up because of the things you saw from Divock in the first half-hour -- we needed his speed.
"Christian came in, it was not easy the first 10 minutes, and second half it was much better.
"He fought intensively and worked hard for the team and he made his goal. He did perfect in the situation."