It's a bit hard to judge how things are with just one game to go by. It also depends on what civ you were playing, how you were playing, who your opponents were and numerous other things. If you were a cultural civ or focusing on culture while none of your opponents were, then an easy culture win is very likely.
I play sort of opposite, though, I love huge maps (or bigger). My current game is with Phoenicia on a Gigantic map with 15 other civs. And I am currently second place in culture while pretty much ignoring the culture game. I have maybe 4 cultural districts now, in an empire of some 25 cities, I've had one Great Writer so far. The leader is Kupe who I doubt is even trying, given how much culture they can inherently generate. I've played some smaller maps (mainly to ding the achievements), but I don't like how limited they feel to me.
In the end, though, only you can really judge what works for you. Maybe try larger map sizes ... more opponents to work against may up the challenge for you without it feeling restrictive in how to play the game. Or give Immortal a go and see if that fits your playstyle. From my understanding, playing on the higher difficulties is mostly a game of working to overcome the initial advantages the AIs get (extra settlers and technologies). I don't play on Immortal or Deity just because I don't like the inevitable initial rushes if I don't focus on my military enough. King is my usual setting for a laid back experience, and Emperor for a more active game.
Or try a couple more games at your current settings to see if your one culture game was just a fluke or that it is just too easy for you. At least they should be quicker games so you'll find out fairly soon.
