You might need a bit more moisture, depending on what you mean by "little damp". We can't get a burnish with the stamps unless there is enough, but not too much, moisture inside the leather. There are many different methods to case the leather, a simple search of "casing leather" on youtube will give you plenty of options, but most of them agree, get it damp enough until it doesn't absorb the water quickly, and then wait long enough for the leather to begin looking like it's dry.
Of course, too much moisture has its own set of problems, like mushy imprints and cuts, but judging from your statement, I would try more water and a bit more time to let it penetrate to the center. Trial and error will find the right moisture level and technique.