That's right. You don't need Mbps, you need better ping. Ping is significantly more important than bandwidth (Mbps). Basically ping is how quick, in terms of ms (milliseconds), you are able to receive a data packet you sent to some far off server. The quicker the better.
Bandwidth, which is measured in terms of Mbps (megabits per second), is a different thing. Basically it's how much data you're able to send within 1 second. In a perfect world, you'd expect to see 2.26Mbps every second, constant and smooth. In the real world however, the data stream is never constant and smooth. It works through "bursts" of data. So something like 2 seconds of nothing, then 3 seconds of high speed download. Averaging that out comes to the value you expect.
Gaming uses some bandwidth, but it is usually minuscule compared to your full connection. You'd actually be fine gaming on a 150Kbps connection. What is more important is ping. Unfortunately ping is almost never advertised when shopping around. And the reason is simple, ping varies from game to game, server to server, from time of day, and from location to location. Your best bet would be to ask around from others using the same ISP service, and playing the same game.