Rodgers did praise their performance, City twice cutting the deficit to one in the second half as part of an attempted comeback, but on both occasions immediately conceding.
Rodgers said: “It was a mixed bag for us today. We had some really good moments but in key moments of the game, we made mistakes. At 2-1, in a good place in the game, and at 3-2 with 15 minutes to go, we've changed the shape and have good momentum, but we concede. It was disappointing in that aspect.
“We started well, were really aggressive and concede just before the drinks break. It's a great finish but we can do better.
“For the players, they kept going right to the very end. If we don't make the mistakes for the goals, then the scoreline is much closer."