Romans did not have a zero at all
The zero actually predates the Roman Empire: Mesopotamia had a zero placeholder thousands of years earlier, and the Mayas invented zero in Roman times.
Romans lacked a good number notation and zero. But nevertheless, the Roman Empire was quite advanced and very viable. It existed nearly 500 years, leaving architecture, laws, iron technology, literature, chronicles, bath houses..
In the Roman case, the zero would probably not have saved them: the Roman Empire was also corrupt and vulnerable for invasion. In 472AD it ended. But it did have fleets.. and a strong army!
The main limitations of Roman numeral notation persisted until medieval times in Europe: not using zero hindered trade and finance calculation. There was no easy way to write and interpret Roman numerals quickly, or denote accounts in an intuitive way. Mesopotamian civilization had bypassed the Romans in accounting, thousands of years earlier.
The Khalifate did discover the zero and a 10-based notation, a few hundred years later.
No physical modeling? zero is not needed
A technology level predating Isaac Newton will hardly experience limitations. A design can be done using a drawing. Then you make a parts list and build your architecture. A Roman, advanced construct is the Partheon dome mentioned by AlexP in the comments. An advanced medieval invention that predates the zero: eye glasses.
While Roman engineering focused on straight forward mechanics and skill, not needing models or graphs, or even tables, the modern way of engineering needs a design, and model calculations. These cannot be made without algebra and algebra cannot really exist without zero. Not having a model or underlying physics to rely on will put airplanes, steam engines, and most mechanization out of reach.
Use of Greek
A remark made below by AlexP required some research. In the Roman Empire, especially the late Roman Empire, often Greek language was used.
Latin was the official language of the Roman Empire, but other
languages were regionally important, such as Greek. (..)
After all freeborn male inhabitants of the Empire were
universally enfranchised in 212 AD, a great number of Roman citizens
would have lacked Latin, though they were expected to acquire at least
a token knowledge, and Latin remained a marker of "Romanness".
In the Eastern empire, laws and official documents were regularly translated into Greek from Latin. Both languages were in active use by government officials and the Church during the 5th century. From the 6th century, Greek culture was studied in the West almost exclusively through Latin translation. Latin loanwords appear liberally in Greek texts on technical topics from late antiquity and the Byzantine period
There is no positional (placeholder) zero in Greek numerals, only an absolute zero value,
Hellenistic astronomers extended alphabetic Greek numerals into a
sexagesimal positional numbering system by limiting each position to a
maximum value of 50 + 9 and including a special symbol for zero, which
was only used alone for a whole table cell, rather than combined with
other digits, like today's modern zero, which is a placeholder in
positional numeric notation. This system was probably adapted from
Babylonian numerals by Hipparchus c. 140 BC. It was then used by
Ptolemy (c. 140), Theon (c. 380) and Theon's daughter Hypatia (died
415). The symbol for zero is clearly different from that of the value
for 70, omicron or "ο". In the 2nd-century papyrus shown here, one can
see the symbol for zero in the lower right, and a number of larger
omicrons elsewhere in the same papyrus.