How can I see how many league games I lost in Starcraft 2?

Use sc2gears to analyze your own replays. You can do a search filter on 1v1 "AutoMM" game types and do a multi-rep analysis which gives you all the statistics and graphs you could wish for, including win/loss/ratio.

I think this illustrates why it's important to keep all of your replays: Battle.net is not an open data source; they can show / hide anything any time they want. To see un-tampered-with analysis of your games, your replay archive is the best source.

It's too bad sites like http://sc2ranks.com will also hide the losses; they should theoretically be able to deduce your loss count from your recent games played even though battle.net doesn't give that metric explicitly. I guess it's not 100% guaranteed accurate...

[update] More of a commentary to your question: As far as "Am I doing well?" honestly your win/loss ratio is of little use, because battle.net tries to match you with equally ranked players (thus trying to keep your ratio ~50% no matter your skill level). If you are improving faster than your moving MMR rating is rising, the ratio will theoretically go up, but that's only in theory. Bnet could just as easily randomly pair you with 10 favored opponents you will lose to.

Another reason why win/loss ratio is a bad metric to judge improvement: Part of getting better is to focus on the things you're bad at, which means during practice you will not win as often. As most of us "practice" on the ladder itself, our win/loss ratio would inaccurately imply that the more you practice, the worse you are.