Going to be away for at least an hour, but the short version of my thoughts are that trading away Ironbark Treant was probably a mistake and—while I don’t have time right now for any specific examples of how you could have done it in this match—it’s important to always try to set up your patrol so Red keeps as few of its attackers alive after their attack as possible. Once I get back to my computer I’ll probably also want to look and see if you had any better options on your first two turns given the hands you had at the time.
Edit: @Azuset, I’ve added some thoughts on the first three turns.
Thoughts on Turns 1 and 2
Let’s start by putting your first two hands here for reference:
Ironbark Treant was a fair play here, and patrolling it in Squad Leader was correct since I wasn’t going to attack with something that had more than 1 HP (unless I did something crazy like Charge an Ogre, but then I wouldn’t have enough gold to build Tech I). An alternative opening might have been Tiger Cub and a Hero, with your Tech I waiting for turn 2. Cub and Calamandra in particular would be strong if I couldn’t kill Cala quickly since the threat of her using stealth to get a hero kill might force me to build a Tower instead of keeping the pressure on you. I could have gotten past Cub to kill Cala with the hand I had, but that would require two cards from my hand and 4 gold, meaning that if I still hire a worker I’m down to 4 cards in my next hand and don’t get a Tech I, plus the only thing on my board is a Lv. 3 Drakk.
Turn 2, I think, is where you hung yourself… And I must confess that if you read my thoughts, I’d intentionally given you the rope to do it with! 
Before anything else, I’m not sure I agree with your tech choices for this turn. Tiny Basilisk and Giant Panda are good cards, but I’m curious why you picked them specifically… With my Dog and Ogre threatening you, a card that can’t block Tech 0 units like Tiny Basilisk seems like it would only be useful to attack, and that assumes it gets a chance to attack. Meanwhile, while Giant Panda didn’t get played, it has the problem of only giving you a 0/1 on defense the turn you play it, but you still have to pay 3 gold. Yes, getting a total of 5 HP for 3 gold is pretty good, but the lack of immediacy for most of that can get you in trouble if Red is putting a lot of pressure on you. Though it does have the advantage of being less useful as a Kidnapping target… (Speaking of which, Tiny Basilisk is a pretty good Kidnapping target since that could potentially let the Red player take it, walk it past your Tech 0 patrollers and trade it with your hero).
I think keeping Ironbark Treant and patrolling it in Squad Leader would have been a better choice than trading it for Bloodrage Ogre, since it would be impossible for me to kill it with only a single attacker unless I did something to give haste to a Taxman or Firebat (and that would cost two cards for one attack, so it still would be good value for you). For that matter, I think casting Forest’s Favor on Ironbark Treant instead of playing Young Treant might have been a good move, since that would guarantee that I would need at least two attackers to get through 3 HP and 3 armor, both of which would die if they had 2 HP or less. Even if I’d gotten through that and killed Arg then, I wouldn’t have as many units alive later, and that’s really important – every unit that Red can keep alive to attack another turn is often a free chance to kill one of your patrollers. Also, it’s worth noting that trading Ironbark Treant for Bloodrage Ogre got rid of a unit that cost you 3 gold to remove a unit that only cost me 2 gold, or 1 gold after the scavenger bonus.
I’ll admit I’m theory-crafting a bit here, partly because I’m tired enough right now that I don’t want to run through all the scenarios, but if you’d just played Arg + Prospector + Forest’s Favor and patrolled Ironbark Treant in Squad Leader and Prospector in Technician (to get back to full hand size if I get through), that would have gone better for you.
Thoughts on Turn 3
I think the game was effectively sealed at the end of your Turn 3. As a reminder, I had just wiped everything off of your board without any casualties on my end, meaning that I had three units and a hero to attack with without even playing any more cards. One of those units was even Makeshift Rambaster, which specializes in destroying buildings. With that in mind, spending 4 gold on a Tech II building you couldn’t defend was a huge mistake.
To be fair, since you didn’t realize that losing both Tech buildings would prevent you from rebuilding Tech II until Tech I was operational again, I could see the logic of “spend money now so I can focus exclusively on defense later.” I’ve even done that kind of thing myself before, but it rarely worked out all that well… I think if you’d played Giant Panda instead of building your Tech II, especially if you’d done the play I suggested for Turn 2, you could have defended better and threatened an attack from the Panda next turn (so I’d be forced to deal with it somehow instead of focusing on your buildings). Heck, you probably could have put Tiger Cub out too to be extra sure.
Squad Leader:
Elite:
Scavenger:
Technician:
Lookout:
Base HP: 20
Base HP: 20