Is there a trick to making the score sound less "computer-generated"?
Certainly. As you may know, most of the music produced today, including pop songs and movie soundtracks, are computer generated. Only the most famous singers and feature films can afford to hire musicians to record their music, because it is so expensive. The general audience will not realize, although subconsciously they may find the recorded music "better".
You are looking into a profession on its own: music production.
(...) yet they obtain much more human sounding results
The music production process takes years if not decades to master. A 4-minute soundtrack may take a team of 3 engineers a month to produce, using hardware and software that easily add up to hundreds of thousands of dollars. If you are just starting out, do not be disappointed if your soundtrack is not nearly as good as those you would like.
The first step is to get a Digital Audio Workstation software, or DAW for short. It is unclear from your question whether you already have one, or you are just rendering sounds from the score software directly.
The second step is to get a good virtual instrument. A high quality virtual instrument library is very expensive. Garritan Personal Orchestra is good for beginners for its low price and simplicity, however you will not have detailed control over note articulation, breathing, vibrato etc.
No matter what library you use, you need to experiment its full potential. Open up the DAW, fire up the instrument, fiddle the settings then play it on a keyboard. Observe how well you can emulate a human player and produce notes with a variety of tonal characteristics.
(...) longer notes are perfectly sustained for long periods of time
(they do not decay)
The third step is to play every instrument, line by line, into the DAW and record the data. This is the core reason why your sound is "robotic" - a real human player will interpret the melodic line and play them musically. If you simply dump the MIDI data from the score software into the DAW, it will always sound robotic. This process will take time, but it will greatly improve your soundtrack quality even if you are using a very cheap virtual instrument. There are "humanization" features in some software, which basically randomly offsets some values, but my opinion is that they don't quite achieve their objective.
For this you would need a MIDI keyboard, a pedal and an ASIO sound card. For entry level options these hardware should be affordable if you can afford GPO.
The next step is to fine tune the performance data recorded. You will need a few hardware fader controls, which is included on most MIDI keyboards. You will at least want to fine tune the "velocity" data of the MIDI, which controls loudness. If your virtual instrument can control vibrato, great. If it can control legato vs staccato, even better. These parameters can either be recorded together with the performance or recorded on a separate run.
This step is optional: If your orchestral score calls for 2 instrument, record them using different virtual instruments. In the real world, it is very unlikely that both flutists are using the exact same flute model. If you "render" the sound directly from the score, the software will just double the volume of the same instrument, which is not realistic. The same principle applies to the entire woodwind and brass section ... I hope you see now why music production is time consuming and expensive.
Then you need to "mix" all your instruments as audio data. In a real orchestra, some players will sit closer to the audience / microphone and some further away. They will have different reverb and left/right balance in the 3D space. When you render the score directly, every instrument is played as if it is right next to the microphone, which is why it sounds unreal.
I hope this answer gives you an idea of how to make your soundtrack less "computer generated" and more lively, and some general directions if you wish to explore further.