I was too late for your match, but I did spectate it for a bit to see if I could give you some pointers. Most of this will come over time, don't worry.
-Don't attack the enemy creeps when they're at full health unless you're actively going for a tower. If you damage the enemy creeps more than necessary, your creeps will win that clash (instead of the usual draw if left untouched), walk further, and start attacking their next wave of creeps. This means that the 'creep equilibrium' is now closer to their tower, which means it's hard for you to kill them and easy for them to kill you. You should still go for that last hit on enemy creeps to earn cash, but leave them alone the rest of the time.
-Be sure to buy the items you want as soon as possible. The longer you're sitting on those 2k gold, the more potential you waste. Plus, if you spend your gold you won't lose as much on death. Whenever you notice your gold count reach four digits, back off a little and open the shop screen, see if you can buy what you want, buy it, and ship it over to you on the courier.
-It's good you're learning denying, but keep in mind that for a gold-hungry carry, last hits are more important than denies. Deny when there's nothing else to do at the moment, but keep your concentration on the last hits and let your support take care of the denies.
-Try to glance at the minimap often to see if any allies or enemies are 'rotating' (switching lanes), looking for a gank. At one point you went back to base to tank up on mana, but at the same time your rubick was coming to your lane under the effect of an invisibility rune. If you had stayed in lane and assisted your rubick (get one last spell and some autoattacks in), you could have made a succesful gank.
