nice attempt, but if I am looking at it it's easy to spot out that the whole palette is to green and it looks - as you remarked - flat. Another problem is that the perspective seems to be somewhat off and that your foliage texture is rather rough.
I also don't read your tutorial (link would be great) so it's pretty hard to imagine what you did wrong - or if the tutorial isn't a good one.
So what would be the best thing to do? step I and II should answer your questions, step III-VIII just show you some of my ideas - trees are always a nice thing for exercising.
I: block it at first out with raw forms, this shouldn't take very long but if you are creating different sprites like this you can choose your best one - give special attention to the perspective.
II: try your raw shading, if your raw shading looks weird the end product will look weird.
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III: if your raw shading looks ok you can work with all those lights you want, the sunlight, the reflected light through the leaves, the reflected light from the ground and so on - train your eye and look around in reality to learn how those light phenomenas are working. The color strongly depends on the light, there is no tutorial for coloring, you can use a reference or thrust your experience.
IV: now you can start with filling in your raw texture, at this time it's more important that you get the right forms and the right impression that you work clean
V: it can be that you did to much, you can test to remove colors and compare the result, in this case the highlights were to bright for a tree
VI: now you can rework your gradients/raw textures. Don't use to much single pixel details, bigger pixel clusters are the way to the goal. Also an important thing to mention is that you shouldn't overdetail it - forms are more important than details
VII: At this point I start to give the outline minimal detail, to underline the impression of foliage.
VIII: FInal color adjustments and contrast/brightness adjustments, this point strongly depends on your scenery
I added next to the last version of the tree yours again, just to show you all the differences - mine has 11 colors, also 3 only colors more than yours.
What to mention is that you keep the pixel art basics (clusters, AA, Banding...) in mind and the drawing basics (perspective,light/shadow,...)
If your drawing or pixel experiences aren't enough to get a good result you should start with studies from nature or from photos. A tutorial will give you only a few insights and you are mostly copying steps you don't really understand.
Or it's also possible to compensate experience with a simpler style or a smaller size, for example -possible isn't a guarantee that it'll look better.

or if you want to do a small and simple variation:
