Liverpool's fifth loss in 11 Premier League matches left them eighth in the table with 18 points and a goal difference of +1 going into the international break, while City moved up to second, closing the gap to four points behind leaders Arsenal with another commanding performance.
Erling Haaland opened the scoring before summer signing Nico Gonzalez doubled the advantage with a deflected strike, and Jeremy Doku sealed the result late on.
Slot had kept faith with the same starting line-up that beat Real Madrid 1-0 in midweek and Aston Villa 2-0 the previous weekend, but City's control of possession and movement through midfield exposed Liverpool's structure early.
"It's easy for players to win their duels if the game-plan and tactics are working," Slot said. "What I did against Villa and Madrid worked really well, but today we struggled a lot with City bringing so many players into the centre of the pitch.
"It wasn't about my players not wanting to compete. They had to run a lot because City were so much better on the ball. That made it difficult to make the right decisions at the right moments.
"I would look to my game-plan first and not blame my players at all."
Liverpool improved after the break but failed to convert several promising moves into goals. "In the second half we deserved a goal," Slot added. "We started winning more duels and recovering the ball better, but we couldn't take our chances."
The Dutchman acknowledged City's superiority, saying: "They were by far the better side in the first half. They were sharper, more composed, and their quality showed in all three goals. The first and third were not huge chances, but that's the difference, their quality in key moments."
With fixtures against Nottingham Forest and West Ham to follow after the international break, Slot will hope Liverpool can rediscover the form that brought back-to-back wins before this setback.
Chelsea ended the weekend on a high with a 3-0 victory over Wolves, but the win was overshadowed by fresh injury concerns as Enzo Fernandez and Joao Pedro both requested substitutions late in the game.
When Belgian forward Leandro Trossard struck to put Arsenal ahead in their 2-2 draw at Sunderland on Saturday, it was hard to remember that just months earlier he had been cast as a sale candidate.
Pep Guardiola celebrated his 1000th match as a manager in fitting fashion on Sunday, guiding Manchester City to a commanding 3-0 win over Liverpool at a rain-soaked Etihad Stadium.
Rumours coming out of Spain are suggesting that Real Madrid and Liverpool are considering a swap deal that would see two superstars switch teams.
