Objectively speaking, sounds are produced by the particular topographical features and movements of the mouth, lips, throat and tongue used in their formation. It's important to understand that even when a single individual makes a particular sound more than once the sound waves they produce are similar but not identical. Because of this, we know that the human brain does not distinguish sounds by their unique sound signature but by the distinguishing features of the wave.
In the field of linguistics we classify these distinguishing features according to the particular features and movements used in their formation. For instance we refer to the breathy sound produced by an open mouth and non-vibrating throat (most commonly heard after "k", "p", and "t" in English) as an aspiration. Try saying "p" as in the beginning of "pop" without moving any air through your throat (I think you can probably hold your breath for half a second). This is an unaspirated "p". Now make the sound the way you would normally say "pop". Can you feel the air moving in your throat? We refer to these two distinct sounds as allophones.
However, we tend to think of these two sounds as being the same thing. This is what we refer to in linguistics as a phoneme. Now get someone else to practice saying "pop" with and without the aspirated "p". Close your eyes and have them say both a few times in no particular order. You felt the difference in your throat. Can you hear the difference in the word? You probably can. When two or more sounds are thought of as being the same but you can actually hear the difference (as in the case of "p") you're dealing with what are referred to as complimentary allophones. They're called this because the sound difference is determined by its position relative to other sounds so the two sounds never occur in the same place. If you couldn't, then you'd be looking at what we refer to as "free variation"; meaning that the sound difference doesn't affect the meaning (or intelligibility) of the word. If the sound difference affected the meaning of the word, this would be referred to as contrastive distribution and means that the sounds are part of distinct phonemes.
Obviously the potential set of allophones is huge, as this incomplete chart demonstrates, so any natural human (real-world) language is going to have some set of phonemes that reduce the number of sounds that need to be distinguished. What allows a phoneme to exist is the similarity of the formative features used to make it, however what makes it into a phoneme instead of an allophone is the inclination to ignore one or more specific formative features that distinguish them. When this happens only depending on the phonetic context (what other sounds are around it), they are complementary and other sounds with the same feature distinction will likely be complementary in the same position as well. If the formative feature is ignored regardless of position (the allophones occur in free variation), then allophones with the same distinguishing feature will likely occur in free variation as well.
Human beings are actually born with the ability to distinguish all allophones from one another, but lose the ability to distinguish them over time (presumably as part of the language learning process) eventually solidifying themselves into the phonemes they've been exposed to. The age at which this happens varies but it universally occurs before kindergarten. This is why we can almost always tell the difference between a natural language and secondary language speaker. A good example of this is how many Asian English speakers have trouble differentiating between "l", "r", and "w" because their native language doesn't do this. Also as a result of this a child who is frequently exposed to multiple languages at an early age will have an easier time learning those languages and will have the potential to speak them as though it were their native language.
Of course, all of this is unique to the way the human brain works. An alien brain would have to work in the same way as our own (an unlikely coincidence) for this to be relevant. But let's assume they just happen to. There is a phenomenon in the human brain known as "allophone restoration" whereby white noise is interpreted as the missing allophone in the word. This is a symptom of the human brain's insistence on pattern formation. What I'm getting at is that an alien with a differently functioning language production method (such as a differently shaped mouth) may indeed make different noises that humans would not be capable of. However, without exposure to it from an early age a human would be unlikely to distinguish between those sounds and may even interpret them as sounds from their own phoneme set. A good real-world example of how this might work for your language are the Khoisan languages, a set of languages that use clicks as consonants. No non-native speaker is likely to appreciate the difference between various forms of clicks. Imagine what that would be like with a creature who's sounds you couldn't actually reproduce.
The short answer is that there's a reason that various science fiction shows use near-human aliens, universal translators, or simply ignore the issue of the language barrier entirely. Think about Star Wars. Not all the languages sound like something humans could speak (particularly Wookiees) yet the various characters often understand each other just fine. I realize this probably wasn't quite the answer you were hoping for but I hope it helps you in your pursuit of scientifically plausible alien language construction!