Just a few notes(Mage is not my main but it's a HC raiding alt). Firstly, the mages you've seen firstly probably have more crit and secondly likely have 2p t14(+8% Pyro dmg) and Pyro also scales much better with Int/Spp than Fireball.
You weren't using Evocate every time your buff dropped off, which you should be, you should also hard-cast Pyroblast if the dot falls off(this includes beginning with it, or using it as your 2nd spell after Mage Bomb, if you can't pre-cast it), both of these tidbits are in the well constructed Fire Mage guide on these forums.
Nothing wrong with your rotation that would lower your pyro-count. It's only a matter of gear from now on, gear will greatly improve your intellect which will give you increased crit chance in addition to the higher numbers of crit rating that you will aquire. Replacing your trinket alone would provide almost 1% crit...
What you can do is change some of your gems, full crit in yellow sockets, crit-int (or possibly crit-exp if more hit is needed) in red sockets, and crit-hit in blue sockets would net you slightly more. It will probably cost you some hit so maybe your gear just isn't ready for it yet...
You can enchant gloves with expertize to free up some hit btw... Leg enchants perhaps?
Is a half decent site to guide you to gear that you could improve. Your bracers comes to mind for instance.
One thing to get more !Pyroblasts in is to NOT use your HS immediatly... but only when you have a Heating up proc as well, in particular the first 2 Fireballs after using Inferno blast to proc Hot Streak.
During these 2 fireballs you have a chance to proc Heating up, but cant promote the proc to Hot Streak... because the Inferno Blast is on cd.
Well you can but you have a 45% chance of doing so... If you have your Hot streak still up, with Heating up too... You then cast Fireball > !Pyroblast givnign you a 70+% chance of procing Hot Streak, which then is Instant Pyro asap because IB is now of CD and you want to use IB to promote your next HU to HS.
So: Fireball 1 (Crit) > Fireball 2 > Infernoblast (before FB 2 hits) > Fireball 3 > Fireball 4 > (No later than here) !Pyroblast
The IB GCD of 1.4 seconds + 4 seconds for 2 fireballs and 1.4 for !Pyro again gets you to 7 seconds of the 8 second cd of IB, your next Fireball therefor should be "IB-promotable" or even if your !Pyro crits you can also IB promote the HU you have then.