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On Wikipedia:

The number zero did not originally have its own Roman numeral, but the word nulla (the Latin word meaning "none") was used by medieval scholars to represent 0. Dionysius Exiguus was known to use nulla alongside Roman numerals in 525. About 725, Bede or one of his colleagues used the letter N, the initial of nulla or of nihil (the Latin word for "nothing") for 0, in a table of epacts, all written in Roman numerals.

Additionally, on this article:

Although Romans used the word nulla (nothing) to convey the concept of zero, the Roman numerals lack a zero digit in their system.

This is interesting. If the Romans were aware in the mathematical concept of zero, or at least, some concept of "nothingness", then they would have been likely to have a digit for it. However, they didn't, as the two quotes say above.

Well, then what's the reason? Why did they only use unofficial symbols such as nulla or the letter N to represent the concept of zero, and not an actual zero digit?

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    $\begingroup$ Romans did calculations with stones moved along grooves. ("Stone" is "calulus" in Latin.) After the calculation, you copy down the answer: 3 in the hundreds column and 6 in the units column ... CCCVI No need to show zero in the tens column. $\endgroup$ – Gerald Edgar Jan 4 at 13:34
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The digit 0 was not needed in the Roman numeral system because this is not a positional system. The only case when it was used was when the number was actually zero, which they called nulla.
Roman digits have a fixed value independent of where they are in a number. For example, the letter X means 10 per se. Its value is added to the other digits in a number, with the exception that if it comes before a higher value digit it is subtracted instead of added, e.g. XL means 40 (50-10) and LX means 60 (50+10).
In the Indian or Arabic system however, each digit has a value which depends on its position, e.g. the digit 2 can have the value 2 if it is in the last position, 20 if it is in the next position, or 200, etc... In this positional system you need to fill every position in the number to preserve its meaning. That's why number zero becomes necessary to indicate an empty position.

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