AQ near the bubble... did i play this correct?

[QWIKSNK]

23 people left in a 20+2 180 man sng at PS top 18 get paid

PokerStars No-Limit Hold'em Tourney, Big Blind is t600 (7 handed)

Hero (t4108)
MP1 (t8500)
MP2 (t14318)
CO (t10457)
Button (t14947)
SB (t7121)
BB (t13052)

Preflop: Hero is UTG with , .
Hero raises to t1800, 5 folds, BB raises to t4200, Hero calls t2258 (All-In).

Flop: (t8508) , , (2 players, 1 all-in)

Turn: (t8508) (2 players, 1 all-in)

River: (t8508) (2 players, 1 all-in)

Final Pot: t8508

Results in white below:
BB has Js Jh (one pair, jacks).
Hero has Ad Qh (high card, ace).
Outcome: BB wins t8508.

I think i had to make that move late in the tourney short stacked.

[CybrPunk]

Yeah with 10BB 7-handed it's not likely you'll be dealt a better hand in the next few orbits. Again, just bad luck that you ran into someone holding JJ. Fortunately your cards were live and you weren't that much of an underdog. Such is the way of poker.

I'm pretty sure if you were to assign a range to villain the pot odds would make calling his push correct. A good player would know that you almost have to call in the spot you were in. Could you put the BB on such a narrow range of hands that you would be behind here? You're about dead even with a range of 88+,A9s+,KTs+,QTs+,AJo+,KQo. You'd literally have to tighten the BBs range to top 5% of hands to make this a bad call. Could you put the BB on a tight range of 99+,AJs+,KQs,AKo? This is exactly the range you don't want to call against. If the BB is playing looser than this I say go for it.

[QWIKSNK]