I'd prefer to put things in my own perspective.
I didn't care much at the time since I was all of approximately 6 or 7. Also, I'm an American.
That being said, first of all, I don't and wouldn't have cared since it's one of our closest allies. Sorry, my Argentinian brothers, but a country that's stuck with mine for a long while... you're on your own.
But most notably: The Falklands were a UK protectorate. Not forced to be one, but voluntarily part of that country by repeated popular vote. I would relate the situation (currently) as Puerto Rico (a US protectorate) being invaded by Haiti.
The people there were part of that nation and still wanted to be. The Brits were fully justified in their response.
From what I've gathered, the Falklands still wants to be part of the UK since last reading the complaints they had about their banks being outsourced to African customer service a few years ago. There was a lotta bitchin' that's for sure.