They DID use reinforced concrete. The Colosseum had plenty of reinforcing iron bars used in its construction.
That ain't reinforced concrete at all, just an old trick used since the greek era. The Parthenon has those too. Reinforced concrete only works with steel bars, since neither bronze nor iron are stiff enough to resist the enormous traction* efforts that exist in concrete beams without breaking.
Besides, Romans would never think about reinforcing concrete because they didn't need it. Their preferred constructive systems (load-bearing walls, domes, archs) worked exclusively by compression efforts, which normal concrete can resist on its own, since in those structures traction efforts are negligible. Concrete, being man-made stone, has similar physical properties to natural stone: it resists superbly compression efforts, but will break easily under traction efforts. The need for reinforced concrete arose after the Industrial Revolution when it became necessary to start building large structures based on beams and pillars instead of load-bearing walls, where the traction efforts are HUGE. The romans would have never thought of building a beam with concrete -for them, beams were something you used in small unimportant buildings like houses, and those could easily and cheaply be built in wood. Serious important buildings were built in concrete- using constructive systems where traction efforts were negligible, which allowed them to use concrete. For the romans to feel the need to use reinforced concrete, you would have needed to make them start an industrial revolution, both giving them the need to build large structures without load-bearing walls (factories) and the industrial complex necessary to manufacture steel - which, as I said before, is the only metal whose physical properties can do the trick; standard iron or bronze would not resist the efforts. Anyway, even if they could somehow manage to invent an early Bessemer process [almost ASB] and manufacture even a small, incredibly expensive amount of steel, they would not have the tools to use it. I'm in 4th year of architecture school, and this year's Structural Science course was 100% devoted to reinforced concrete structures. Trust me, in order to make an efficient reinforced concrete structure, you need to have a deep understanding of how the efforts work inside of the beams and pillars, which needs physical and mathematical tools that the romans could not even dream of.
*Sorry if that's wrong or misleading, I don't know the technical jargon in english