Right play, for sure. It's too good a hand to fold. You are in 5th and only 3 get tickets, so it's not like you can sit out. Did utg push or raise and then you pushed? It doesn't really matter, even if he pushed he is pushing with A4, maybe worse, so you had him dominated. Unfortunately you lost, but you got it in good, and you didn't have the luxury of not playing so it's fine. The alternative is to fold and wait till you have a hand to push with no action in front of you, but then you might have to go with a worse spot and end up being called by better.
Satys are hard to judge. I bubbled one the other day. 10 people got tickets and I finished 11th. Sometime you think you are going to make it sitting out, but then some shorties double and blinds go up and hit you. That's a killer, to watch out for. I misjudged the blinds going up, that took me out and someone with 1/2 a blind got a ticket.