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You launch a successful attack, but the opponent is able to avoid immediate defeat by giving up some material. Sometimes the best strategy is to change gears to converting your material advantage instead of trying to keep attacking.
Yup. Good chess is often about managing the game in stages. You've won the opening and now it's time to manage the middle game with a slight advantage. Look for tactics that could benefit you as well as taking into account specific strategic considerations such as dominating open files with rooks and giving your bishops and knights good mobility all while maintaining a solid King area.
If you can do that, you should be in a good position to eliminate material while maintaining your advantage, which will hopefully turn into a winning end game for you.
Also, I dislike the fried liver attack. My preferred defense vs the fried liver is to attack the f pawn with my bishop and attack relentlessly vs the exposed king. I forget the name of this attack but it works quite well. I'm not sure of the theoretical soundness of it but I've won many games as black with it; if they've never seen it before it works great.