When negotiating (and interviewing for a job is a negotiation), never give more information than you have to.
In your case, no one but the recruiter (and other people on the hiring committee) know why you were really rejected; but what's certain is that telling her that you decided to not take the offer certainly didn't help you.
However, saying something like: "Microsoft's offer is really enticing, and I'm thinking very hard about it. That being said I've heard so many great things about Google, and I'd love to work there. Microsoft wants my decision by <end of month, end of next week, whatever>- do you think we could go through the interviews before then?".
That alone wouldn't have gotten you an offer, but it would have made you a slightly more desirable target.
Keep in mind that interviewing is ultimately a human thing, and thus never perfect or rational (even though everyone would like to think their hiring process is flawless and as logical and unbiased as can be).
Prepare as much as you can, go in with your best attitude, etc.- but at the end of the day, interviews can result into a negative answer for something completely out of your control. Maybe you remind one of the interviewers of their ex-boyfriend, or they don't like your voice on the phone, or they've never used framework X but the guy they just fired was really into X and you put X as the first thing on your resume, etc. etc. etc.
Don't get discouraged- it's part of the game. I am starting next week at $(big large company where I've wanted to work since I've been a teenager), and that was after 6+ months of interviewing, talking to about as many teams, and hearing "we think we'd be really great at $company but the team you've just interviewed with isn't the right team for you" every time. Funny thing, the position I ended up getting is beyond what I could have dreamed of 6 months ago, and far more interesting+challenging than any of the other teams I interviewed with there.
There's also nothing wrong with working at a company for a year or two with the sole intention of getting better so you can re-interview with the company of your dreams.
Work hard, keep your long term goals in mind, and good luck :)
In your case, no one but the recruiter (and other people on the hiring committee) know why you were really rejected; but what's certain is that telling her that you decided to not take the offer certainly didn't help you.
However, saying something like: "Microsoft's offer is really enticing, and I'm thinking very hard about it. That being said I've heard so many great things about Google, and I'd love to work there. Microsoft wants my decision by <end of month, end of next week, whatever>- do you think we could go through the interviews before then?".
That alone wouldn't have gotten you an offer, but it would have made you a slightly more desirable target.