Since I was going for Pools, I couldn't use Trading Post as my trashing because Silver would be an extra non-action card I'd have to get through.
Well, it's not exactly clear to me what you're saying here. You certainly CAN use Trading Post anyway - the reason you don't want to here is just that Forager is better - it's non-terminal, a decent 3, and there are things you'd like to do on 4 (and to some extent 5). But having silver as an extra card to get through... I mean, yes, it is, but on the other hand, you trashed 2 to start. Trash 2, up 1 is basically equivalent to trash 1.
So I got payload from the various $2-giving actions on the board. My opponent, meanwhile, opened Monument, got terminal trashing, didn't get a single village or +Buy, and pulled off a Minion deck that beat my Pool engine.
This is actually just wrong. He got a forager on turn 2. That's a +buy card. And while he got a terminal trasher, he got as many non-terminal trashers as you. As for villages, not only did he start with Necropolis, he got 3 Throne Rooms. So he has Villages.
The biggest things I see here are 1. Based on what you wrote, you seem to have written off what your opponent did as being bad, which leads to you underestimating what he did, and not paying attention to him. What he did isn't THAT different from what you did, really. 2. I want to say that Fortune Teller is not a good card here. It makes $2, but it's terminal, and the attack does very little against an opponent who is trashing and a you who have scrying pool anyway. 3. You don't have a clear goal as to what you're building to. You have this vague, you are getting terminal silvers. For what? To buy provinces, I guess. That isn't actually all that strong? You should be aiming to play lots of Monuments. And most of all (related to this), 4. You don't build enough. Getting more monuments (and throne rooms to help you play them) is a thing you want to do here. If you can do that early enough, it's going to score more points for you than the green card anyway, while being better for your deck. Also, greening as early as you do not only hurts your deck, it actually mitigates the weakness of a minion deck anyway, that it can't handle bloat very well.
Now, I don't want to say, you got completely crushed or played really badly or much worse than your opponent or anything like that. But there are several little ways you could have improved, and those things really can add up, and most of all, what he did isn't so much worse anyway.
PPE: and lots of responses already.