Actually, the Romans were quiet good in sailing and their ships were state of the art at the time. They had a navy, but a even much bigger fleet of trading ships owned by private people. They travelled all over the mediterranean sea and even as far as Ireland and England to do business. Only their method of navigation limted them somewhat. Mostly they stayed in viewing distance of a the coast line, and they stopped on the coast - preferably a harbor - for the night. Crossing open sea areas was usually done on certain fixed routes that they knew from experience.
May be some tried to head out west into the atlantic, but after finding nothing after a few days they turned back.
Its a fundamental problem for all explorers: a discovery is only of value, if you are able to return home and tell about it. May be a whole number of people, Egyptians, Romans and who ever, made it over the Atlantic, more or less intentional. But they never made it back again. Perhaps thats the reason for the egyptian artefacts in Brasil, too.
Well, today the excitement is somewhat lost in the whole exploring thing. Even different planets like Mars, we know already what it looks like there, before anybody ever set foot on it. That makes it much less adventurous, although its still dangerous to go there. But thats more because of technical problems, rather than facing the unexpected.