the 2 biggest rules in Omaha (especially Omaha Hi) :
1) never over-estimate a pair on your starting hand even a big one ( if you don't flop a set then fold it as quick as you can)
2) never slow play a good hand you hit on the flop (set but moreover straight, flush and so one) as it is likely that somebody on a draw will hit a greater hand on turn or river. As you don't want them to do so you have to discouraging them by betting hard : they should have to pay a lot for hitting their cards.
Your opponent feels strong enough with his pockets aces to call your raise (which was a big mistake). However he was lucky enough to hit both turn and river.
There is nothing you can do about that as as Alan said once he hits his third ace you even can put him all-in he would have called you.
PS : I forgot to say that your table position is also important at Omaha (but should I really need to say ...
)