It's not the game's issue bro, it's your TV. I'm guessing your TV is older since it doesn't have game mode (Come to think of it, I don't even know when game mode was first introduced). If you're playing online only, maybe it's server lag, in which case I'd say try a single player game to make sure, but if it lags like that offline too, it's definitely your TV.
I highly recommend this site to anyone thinking about buying a new TV, for any reason:
http://www.rtings.com/ They review each TV based on pretty much any category under the sun, and you can search all of the reviews based on price range, so if you want a TV under $500 for example, you can search for all reviews for TV's currently under $500.
I actually just bought a TV last week, and all of my research came from there. I'm extremely happy with what I got, and the info about the TV I got was spot on.
Here's their explanation of input lag, how they test it, a list of TV's rated from lowest to highest response time, and some settings that can be turned off or down to help reduce the lag for TV's without game mode:
http://www.rtings.com/tv/tests/video-games/input-lag
If your TV has any of those settings on, turning them off (or to the lowest setting if they can't be turned off) might be all you need to do. Quick note, they didn't start doing tests until 2013 or 2014, so they won't have any info for models that came out before that. Hope that helps, I know it's kind of a lot... lol.