This is the question of how to hear language sound. I think most of Japanese people hear Japanese words as a sequence of sound units which are the most fundamental. And, I guessed that this was true in English too at first, but started to doubt it recently because weak sounds in English can easily fall off and this means the sound is not necessary so that the sequence of components can easily be changed into another form. What do you think of this matter?
I think what you're hearing is the difference between a mora-timed language (Japanese) and a stress-timed language (English). These are different forms of isochrony, or methods of dividing language into (apparently) equal intervals of time.
According to Wikipedia, Japanese is mora-timed, meaning that each mora, which Wikipedia defines as either a vowel or vowel-plus-consonant, takes the same amount of time to say (and double vowels take twice as long). This is why you perceive Japanese as a sequence of every "fundamental" sound unit.
English, in contrast, is stress-timed, meaning that the (apparently) regular interval is between stressed syllables only. In order to make that happen, any unstressed syllables need to be compressed to fit within the interval. When we have a regular pattern of stressed-unstressed syllables, this sounds fairly distinct (and we call it iambic stress). For example:
The only one I want is you.
the ON-ly ONE i WANT is YOU.
With this kind of pattern, you probably will be able to hear all of the syllables, even the unstressed ones. However, not all English follows this exact 1-1 pattern. When we start to have additional unstressed syllables in between stressed syllables, they need to be said in a way that we can still perceive the unstressed "gaps" as being the same length. So
Long sentences can sound like they're running together.
LONG SEN-ten-ces-can SOUND like-they're RUN-ing-to-GE-ther.
The particular stress pattern might vary a bit depending on the speaker, but the main idea is the same: some of those unstressed syllables will be connected or dropped in various ways (e.g. going to becomes gonna, probably becomes prolly or prob'ly, to the becomes t'th, etc.).
Incidentally, native English speakers are generally not aware of this effect, so to us English does seem like a series of distinct sounds, and other timing systems seem a little bit odd somehow. My own surname is a four-syllable Japanese name; in English, it is pronounced as two iambs, with strong stress on the third syllable and nearly-as-strong secondary stress on the first syllable. The first time I heard a native-Japanese-speaker say it, I almost didn't realize he was talking to me, and it sounded like the final syllable (a vowel) was almost entirely swallowed.
It is said (don't hold me to it, I can't remember where I read it) folks take in about 25% of all the information they receive verbally - including, I would imagine, the Japanese. The rest is either ignored or assumed.
This is in part because everyday conversation is composed chiefly of oft-repeated trivialities. The ear seeks out and focuses on key words, and the brain supplies the rest before the rest is spoken. Thus, certain parts of sentences (and, yes, vowels, consonants, and certain parts of words) can be dropped (and often are dropped) by the speaker without the listener's losing the thread of the conversation.
This is true of all European languages, and I'm nearly 100% certain that in one form or another it is also true of all others.