A simple piece to make your Tetris puzzle look better is to go with the original design scheme tetris used:
Seperate the 7 colours that you will use (these don't need to stay close to the originals at all but may help with attracting those that recognize it's classic colour scheme.) Giving yourself a colour pallette before you have even made your set of shapes can really help and if you are going for the tetris shapes then you only need 7 colours for them.
You can use the fact that the tetrominos are actually 4 squares adjacent to each other instead of one solid shape if you prefer. This will make your design look more diverse but it can lend itself to many different design choices. You can make each segment into a square with bezel, rounding, inset or a border:
You can still apply these effects and styles to a solid tetromino shape and get different effects from it. I know from chat that you use Paint.NET so here are some useful plugins to get you started:
You could also play with segment shapes so instead of a square, do a circle or octagon and that way your background can play a larger part (giving gaps between the shapes will reveal what background you use.)
Ultimately, play around with your design and use some clean up techniques like the others mentioned: my personal favourite being the anti-aliasing. One of the best resources I found you can find here in this Stack Overflow question and here in this blog post that gives you many options. This will quickly ensure a lot of your display looks crisp and un-pixelated which I think is the main source of your issue.
To ensure you keep your apps "ugliness" scale to an all time low do 3 core things:
- Decide on a colour pallete: whatever colours you choose, pastel, solid, bevelled or otherwise - stick with it
- Use anti-aliasing: also called multisampling to make sure jagged edges from transparent or high contrast pixels are smoothed
- Create high resolution images: scaling an image up from a low resolution to higher almost always produces a lower quality. It doesn't matter how simple you make the design, however, use the highest resolution you can whilst being mindful of your resources budget. No need for your tetronimo to be 1920 x 1080 and 1.3Meg, but no harm in making it bigger than 10 x 10.
As an example of what you can acheive with a few minutes in Paint.NET or Photoshop, here is my example:
Where you go from there is completely up to you!