Speaking English well isn't all about pronunciation, but pronouncing words properly does matter. Here's an interesting video about the American "T" sound that I found very useful in all my years of training others to speak English.
American English speakers have a curious way of pronouncing words sometimes because it's important to get the words to connect together, as if you're speaking one really long word. This is sometimes called "linking words" or "liaisons." Because of this rule of connecting words, the way you pronounce the letter "T" in US English can be done in four different ways.
One way of doing it is to pronounce the T as a "fast D." Check out the video and I hope it helps. :)