Any horse can be successful at barrels. It's just a matter of proper training, body placement, sound pockets, and the right kind of riding.
Given the way you go about your pattern I'm assuming you haven't started a barrel horse before. It is really easy to sour a horse on barrels - if he's bucking its a good sign and you're probably not moving in the right direction. The following is just some tips from me to try and keep the pair of you safe while learning how to make a good run.
Your pockets won't get tigher unless you start riding agressively through the pocket. Your horse is just tipping in his nose and not shaping his body. You need to actively shape his body around that can and if necessary circle each barrel until he understands that his body needs to be rounded.
Here are some tips for you:
1. Get nice, even pockets. A pocket is the shape you take around a barrel. You want work your horse at maintaining the same gate throughout the pattern and so that they can bend themselves around the barrel - right now your horse is doing the barrel like a square dance. You need to help him by rounding his body (use your inside rein and round his form with the inside spur if necessary).
2. There is no point in loping between barrels at this point. Your horse can't lope around the can so don't lope him on the rest of the pattern. Loping some parts but not all teaches a barrel prospect that the can is meant to be a slow part - if you get him into this habbit it can take a professional barrel trainer to get him out. You need to jog the pattern maintaining a steady gait the entire time. Do this until you can keep an equal distance (prefect circle) around each barrel.
3. I'm not sure what you've got in that horse's mouth but you need something sidepull. I do a lot of my barrel training in a loose ring snaffle. Get in the habit of reaching down close on the turning side with one hand and grabbing for the horn with your free hand. If your horse ever actually turns hard you're going to be left in the dust.
So - do not lope that horse on the pattern again until he can trot the whole thing with nice, round pockets that are close (not tight , just close) to the barrel. I would think about getting a set of barrel reins if i were you as this will be easier to handle in speed events and many of them have knots to help your hand placement.
Last but not least - NEVER lope back from the 3rd can. This is where a lot of horses get hot heads and you don't want to get him too excited while training. I run a horse straight home from the can only after they have been loping a steady pattern for 6-8 weeks with nice pockets and then I only ask for it maybe once per week.
Best of luck and have lots of fun!
**UPDATE** This isn't an ideal tutorial but it can help you out. There are a lot of sound fundamentals here.
http://www.youtube.com/watch?v=kZbms2Fb7jo