I think the big problem was playing the Barracks forward. You would have been better off opening with something like:
Turn 1 (19): Barracks in start corner -> Garrison Post in NC (3)
Turn 2 (12) [2]: Deploy Orc Butcher -> General's Signet Ring -> Leather Gloves (1)
At this point you have a little bit of defense against multiple attacks, you are in a similar position in terms of overall economy, you still need to play the Armory, but it's more awkward for the Druid to be able to pull all of your small creatures through a Bloodspine Wall into Mangler Caltrops the turn you play them. In addition, you would have put your opponent under more pressure early by getting that Orc Butcher down a turn earlier.
You kept doing little bits of damage, but not focus firing things down. This is especially important against plants, as all plant creatures have Regenerate.
Goblin Alchemists would have been amazing in this match with their fire attack.
If you want to use weak ranged creatures like Goblin Slingers, you're going to need to create more space between them and your opponent's threats.
If you're going to have your mage stay in a zone where you are constantly outnumbered by enemy creatures, you need to do more to shore up your defenses. Armor, Aegis, and Defenses are all options, but you need to do something.
You shouldn't have attacked the Wall of Thorns. It blocked line of sight, and you could have used that as a chance to get away to try and recover.
I don't think it was an issue with your late game so much as never getting your midgame going. I think turn 4 was where the issue of playing your Barracks forward became apparent, and you fell behind because your Slinger was immediately pulled through a meat grinder without getting to do anything. You recovered a little bit with the Hail of Stone, but you really needed to follow up with more durable threats.
