Dumb Bet?

Blinds are 300/600, will be 400/800 by the time I'm in big blind (6 minutes left in the 40 minute round). I have 4800 in chips (8x BB, or 6xBB once the blind flips). People usually say short stacked is less than 10x the big blind.

The guy in 1st position (chip leader with 29,000) raises to 1600, it comes around to me. I had AJ, I thought about folding it since the other guy might have a pair, but since he's a chip leader he could afford a raise with any two paint. I know he'll call if I go all-in so I just called the 1600 (possible mistake). The guy acting after me, who was also short stacked, went all in for about 8k. The chip leader folded and it was to me. I called the last 3200 worth of chips since I know the guy who went all in and he said during the last break that he's going all in on Ax next time he gets it since he didn't want to get blinded out and wanted to go out with a bang instead of dying slowly.

Was it wrong to just call when on short stack? I figured that if an A, a J, or 3 rags hit on the flop I could go all in and feel against the chip leader and feel secure in my bet. If a K, Q, or T hit I could fold to his bet or check it down and still have 3000 left to play with if I lost. I wanted to only call him since I thought for sure he would call me and why spend more than I have to in order to see the flop first? I didn't think anyone else would go over the top. I was right in my reads, chip leader had KQ and the reraiser had AT. However a T hit on the river and I lost the rest of my chips. I feel good about my reads, but wasn't sure if I should have bet more or if I was in a hopeless position. In this case I would have lost either way, but in the long run the cards will come up different.

So next time should I push all-in right away or try to see the flop on the cheap again.