Now I have a network trained to get an output value from an random set of attributes but, can I use this trained network to get the input attributes using only the desired output?
If you are happy to find any inputs, even non-realistic ones, that get your desired output, then you can use your trained network, with a minor modification. Freeze all the weights, and allow back-propagation to determine the gradient of the input (which should now be a variable to optimise, not source data). Start with a noise input, back-propagate the error to find gradient to make the input better at creating your desired output, then take a gradient step towards it in the input data. This is essentially how Deep Dream works. Like Deep Dream, you will not necessarily get realistic input values, but will get semi-random ones that cause your network to predict a specific class.
If you want the newly generated input to be a best guess at something from the original dataset, then you have to look at one of more advanced models:
These network types are quite advanced, and can be tricky to understand and train successfully. You will want to spend some time researching each type.
To generalise terribly: A GAN will tend to generate realistic "noise" in the generated items, but at the expense of overall structure and cohesion (images tend to look distorted but with realistic textures). A VAE will tend to produce smooth, coherent inputs, but at the expense of lack of fine detail (VAE images tend to look smoothed and/or blurred).
If not sure what to try, probably GAN is a reasonable choice, since there are lots of tutorials available, and recent advances with image generation can look very impressive.