The same critique techniques can be used by the artist to evaluate their own work by following a general criteria to look at key points.
Did you convey the inspiration that compelled you to paint the subject? If it was a portrait, does it catch the likeness, or the character? If it was a certain light did you give it the drama needed to be focal? If you feel you did not catch the mood, then it's time to look and see how technique can help in the next piece.
The eye seems to be drawn to certain placements more readily than others. Even though beginning artists tend to plop things right in the middle of the page it's not the best place for a focal point. There are points like on a third mark (mentally divide the page into thirds and place your subject on one of the intersecting lines) that give paintings interest. The Golden Ratio is another method of placement. You don't have to follow an exact rule but the important thing is that there's a flow that keeps the eye moving around the painting. You can control how someone does this by using a lot of different techniques.
Technique is not only about how well you wield a brush or a tool. Art is an illusion and there are ways to manipulate your medium to help with that illusion. Do you have hard and soft edges? This helps the eye move, fades certain areas into distance or less importance and accentuates areas of more importance, bringing them forward. Placing something to stop the eye is important too, especially if something in your work is pointing the eye out of the picture. A well placed solid object can halt that escape.
Are you using color to your advantage? Warms and cools help with depth, contrasting colors bring excitement, harmonious colors keep, well, harmony throughout. Grays made from colors work as neutrals, mud is failed neutrals that jar.
Do you have a distinct focal point? This is not necessarily a complete object...but the 'impact' point of the artwork. To get a good focal point play up that area, subdue the rest to it.
Perhaps this is the most important part...so much can throw the flow off...a line/edge that is too long or short for proportion, an angle that isn't quite right on a shape. Look for what you don't see, negative shapes are just as important to flow as what a viewer can see.
Using the critique
Perfection is unattainable, but improvement on the next piece certainly is within your reach and if you fairly critique your work and use it to improve, then it has an accumulative effect over time. You can't fix everything at once. Choose one thing to work on, research it, practice it, use it to advantage until you've 'got' it. Then move on to another area to work on. Before long you will see an overall improvement on your work and you will have the necessary skills to create any illusion you want.