I now see I misread your explanation. I thought you were saying Armenia started the war but I see you're saying Armenia had a disadvantage from the beginning. (sorry about that)

But I still want to point out that this war was between the Artsakh(Karabakh) Armenians and Azerbaijan, and not Armenia directly.

I'm sure the mods will know how to handle this properly but I wanted to point out that even though the wikipedia article on the war says it ended in 1994 there is still a conflict going on, in a sort of stale mate, with sniper fire across borders killing someone as close as a month or two ago.

There are still many displaced Armenians, Azeris, and Kurds living in Artsakh as well as in surrounding countries unable to get back in.

I'm not an historian, but I think it has got a lot to do with the unofficial support the Armenian side got from the Russians. There have been numerous reports in the (especially Western) media about Russia delivering weapons and tanks to the Armenian side. These reports have been criticized, because Russia helped the military of Azerbaijan during the conflict as well. Armenia and Russia have denied these allegations too.

However, the Washington Times argued that the Russian weapons played a crucial role in Armenia's seizure of large areas of Azerbaijan. They also suggested that Russia's military support for Armenia was aimed to force "pro-Western Azerbaijan and its strategic oil reserves into Russia's orbit".

I've got this information from various sources, including this Wiki page. Considering my background (and my sources), I'd advise you to take this with a grain of salt until a proper historian can respond to your question adequately.