Rafa Benitez said: "The game was very frustrating, we tried to play wide, we tried to get the ball into the box and we did everything we could to break them down.
"In the end we ran out of ideas. The game was too narrow, it was too congested in the box and there was no space.
"Credit to Birmingham, they were very well organised and worked very hard. They made it very difficult."
Benitez caused a surprise beforehand by leaving £20m striker Fernando Torres on the bench for an hour.
He defended the decision, saying: "I have four strikers, I played them all in the end.
"I felt that Andriy Voronin and Dirk Kuyt were the type of striker I would have needed to work hard against a packed defence."
Benitez said: "I do not think it is too serious, but we will have to see about him for the midweek cup tie."
And the Spaniard accepted that Birmingham's deep defensive system is something that many teams will try to imitate at Anfield.
He said: "Yes, I suppose we must expect that style of play.
"But it is up to us to break it down, to find the spaces.
"It would have been a different game if we had scored from one of our early chances, but as each minute went by the situation became more difficult for us."