Keep in mind that there are a lot of sprite collection websites which offer assets with dubious copyright status. Unfortunately it is pretty common to "rip" sprites from commercial games and place them on websites without a copyright message. Or even worse: a copyright message crediting the person who ripped the graphics instead of the legitimate copyright holder. The website you linked is a good example - almost all assets on there are from commercial games. When you release a game with those graphics, you are committing a copyright violation, and you are risking a lawsuit!
So what are your options?
There are some repositories of graphics which are really free. One repository I know is http://opengameart.org/ which has a lot of assets under Creative Commons licenses. Unfortunately all assets which are really free are already pretty overused, so you won't impress people much when you build a game from them.
Or you could hire a graphic artist. There is another question about that:
How do I find artists to work on my game?
Or you could learn it yourself. Pixel art isn't really that difficult to learn. You usully don't need sophisticated tools for it. Any raster-oriented graphic editor would do, even MS Paint is sufficient for a beginner. Here is a great tutorial:
"So You Want To Be A Pixel Artist?" by Tsugumo (over 10 years old, but still very relevant)