Google is probably using information that it has not specifically requested of you during the password reset process in order to verify your ownership of the account. Specifically, tokens stored on your computer, and your IP address.
I had a similar experience to yours, which initially alarmed me, and tested the above theory by using the Tor browser to perform the reset. This browser redirects a Web session through Tor's own servers in Europe, making your session more anonymous.
The result was a much more aggressive set of questions. The first time I attempted to reset the password, I just blew them off, and hit a brick wall. I tried a second time, and once I had answered the questions somewhat correctly, I was presented with an emailed link to a reset page. When I clicked that link, since I have two-step verification set up, I was presented with a demand for a number provided by the Google Authenticator app on my phone. I provided that number and only then was I allowed to reset the password.
This experience gives me more confidence in the process. Google, while fallible, is not a huge corporate playpen full of idiots. Password security is a critical feature of Google's business, and I'm sure that they have thought long and hard about how best to allow legitimate users who are schleppy enough to lose passwords to get them back without allowing thieves to run off with all the Google accounts.
Best Answer
No, you can't do that. There is nothing in Gmail's settings to restrict from where your account can be accessed.
Really, you shouldn't have to. Google already does some checking to see if your account is being accessed from wildly divergent locations.
According to the Google Online Security Blog:
If you're suspicious that your account might have been accessed from a place where you haven't been, be sure to check the latest activity on your account by clicking the "Details" link at the bottom of your Gmail page.
There's also this general guide to keeping your Gmail/Google account safe: How do I protect my Google/Gmail account?