A late Mo Salah penalty and a 94th minute Darwin Nunez goal proved the difference in a fiercely contested season curtain raiser at the King Power Stadium.
Liverpool’s Trent Alexander-Arnold had opened the scoring with a curling effort in the first half, before Julian Alvarez’s first City goal levelled the scores deep in the second period.
Having only returned for pre-season on 11 July, City are only in the third week of preparations for the new Premier League season.
With that in mind, the manager was happy with what he saw at this stage.
He said: “We’ve had two weeks and a few more days now since we started but in general they gave everything. I said to the players I am proud of how they gave everything.
“Now, we have to improve. We need this month of training to get our tempo and we will do it.”
City struggled to play with our usual rhythm in the first half, but grew into the game after Liverpool’s opening goal.
Despite not being at our best, Pep still believes we had enough chances to win the match.
“The first 15, 20 minutes they were better,” he admitted.
“They got the pace and after we got our game - it was quite similar the last 25 minutes [of the first half], we arrive when they leave space and tried to attack.
“In the second half we started really well, it was tight after the goal and our game was there. We were really good against this team, even in the first half we created enough chances to do it.”
Erling Haaland played the full match on his competitive debut for City, while Alvarez came on to make his first appearance.
Asked in his post-match press conference about Haaland, Pep said he was encouraged by what he saw from the Norwegian striker.
“He had chances - two or three in the first half and one at the end. Always he was there. He fought a lot and made the movements.
“It’s good for him to see the reality of the new country, new league. He was there. Today he didn't score - another day he will score.”