Don't Huff and Puff...
There are three consonants that speakers of American English tend to pronounce in a way that is instantly recognizable to Spanish speakers as a tell-tale sign of an American speaking Spanish. Those are the consonants C, P and T. The consonant C is only a problem when it is pronounced like a K -- that is, when it is followed by an A, O or a U: CA, CO and CU. When the C is followed by an E or an I in the western hemisphere, it is pronounced like an S. In much of Spain (roughly central through northern Spain), it is pronounced like the TH in the English word thin -- known as theta. It is most definitely not a lisp, as many people like to call it. The same speaker is perfectly capable of pronouncing all S sounds one would expect.
What is an exploding consonant and how can I get you to say one using these written instructions? Well, place the back of your hand about two finger widths in front of your mouth and say, in a normal, conversational volume, in English, the following three names:
When you say these three names in normal, proper English, it is likely that you will feel a slight puff of air on the back of your hand. This is fine -- for English. But if you try saying these names in Spanish:
... and feel that puff of air, then you are "guilty" of exploding your consonants! So, if you're serious about trying to eliminate or reduce your American accent, then here is how to modify the pronunciation. First of all, it does not help much to speak more softly. That isn't the point. It isn't about volume -- it's about the mode or manner of articulation.
Let's learn some vocabulary and the place and mode of articulation. The English K sound is a palatal occlusive -- it is pronounced with the back of the tongue occluding or stopping the air at the middle or near the back of the hard palate. If you slightly relax the tongue so that it doesn't totally occlude the air, making it a bit more like a G -- as if it were Garlos, then you'll probably succeed at reducing the puff of air that launches the K out of your mouth.
As for the English P, it is a bilabial occlusive: pronounced by the two lips closing off the air before launching the P. To get rid of the explosion, pronounce the P a bit more like a lazy B (allowing some air to escape from between your lips), as if it were Bedro.
Lastly, the English T is an alveolar occlusive: pronounced with the tip of the tongue contacting the ridge just behind your upper front teeth. One way to reduce the explosive pronunciation of the T is to pronounce it just a little bit more like the TH in the word though or the D in dough, again, allowing a little air to escape.
The trick really is to not allow these three consonants to be pronounced occlusively, but rather as fricatives -- letting a little air out of the tires so to speak, so you get a gentler ride! Practice the three names with your hand in the same position until you do not feel the puff of air and you'll know you're saying them correctly - without an American accent.