I don't know anything about Civics, but in Accords this symptom w/o CEL indicates the EGR ports are partially blocked. When you lightly accelerate, the additional EG goes to fewer ports and overleans the engine. The result is a flat spot in acceleration. Accords have had this problem since at least the early 90's models. If Civic has EGR and EG distribution manifold, this could be the problem.

good luck