How much damage were you taking in those battles? How much scrap were you spending on minor upgrades (doors, oxygen, medical, shields, etc) or repairs?

A good player can often get through the first sector without repairing at all, without spending a single point of scrap on minor upgrades and fighting as many battles as possible. This lets you buy a big ticket item such as a cloaking device, a teleporter or a powerful weapon right away. Big ticket items (especially the teleporter) have the ability to pay for themselves many times over.

The real beauty and elegance of FTL's design is that it makes opportunity costs a real factor in game play. Buying a lot of small upgrades makes you a lot more survivable early on but severely restricts your total scrap potential over the course of an entire game. The key to winning FTL is to coast along on as minimal a budget as possible until you land a big ticket item and then invest heavily into it so that you can earn more scrap and take a lot less damage going forward. Of course, none of this strategy works if you aren't playing battles very carefully and making optimal use of the pause button to coordinate your weapons.