[...] but is there something I'm missing? I play as Rome on king
A screenshot would elicit the best advise.
The most likely remedy is to change your initial development priorities/execution. There are many "Let's Play" video series these days. I personally like Moriarte's stuff. I would check out either the Denmark game (Liberty opener, pre fall 2013 patch) or the Celt game (Tradition opener).
https://www.youtube.com/user/Moriarte1982/playlists
In terms of how to catch up, Civ 5 actually has many mechanisms.
1) Trade Routes with civs that have a tech lead will yield beakers proportional to the tech difference. Mostly useful early game on higher difficulties.
2) Techs researched by civs that you've met will give a modest reduction in their beaker reqs -> scout early and aggressively. Get that caravel across to the other continent.
3) Spies are probably the single most important technology equalizer. If you are behind throw a spy or several into AI cities. I find the best targets are either: the capital of an AI that has a lead over you, but does
not have the global tech lead; or the largest non-capital city of the tech leader. (To maximize your rate of successful stealing).
4) There is a World Congress proposal "Scholars in Residence" that gives a 20% reduction in beakers for any tech already discovered by another player.
5) There is a bug/exploit that you can use in some situations involving Great Scientists' Bulbs, Scholars in Residence, pre-discovered tech, etc. This is banned in Games of the Month, most MP, etc, & requires several conditions to setup, so use at your own discretion. Yoruus shows a devastatingly effective example:
https://www.youtube.com/watch?v=vaVNdjOGXK4&list=PLgYopQWwsyjG41klZaOVjtuCQ44yiEnvV