Bad play HU?

[Hellrazor]

20+2 Party

Hero slightly covering villian.
Blinds 400/800 (? - memory here)
Preflop 22 to Hero in BB

Villain raises to 1600.

Hero pushes.

Only read on the villain is that he was very tight pre-bubble time and VERY aggressive post bubble.

Villain called and showed AKo- results are inconsequential.

I'm split here as to what my best play was. If I go all-in as I did I have a good shot of my opp. folding. If he does call my best hope is a coin flip and pray he doesn't have any pocket pair.