I've found a solution wherein I traverse the whole downloaded HTML page, character by character, searching for certain pattern. Is there any other way to get the URLs in a simple way, instead of searching for the pattern character by character?

Yes! At the very least you may try a regex, but it wouldn't be a good solution either, and it is generally recommended to avoid it. You'll find that

perldoc -q URLs
[download]

lists some alternatives. In particular I've used advantageously HTML::LinkExtor in the past. And it was quite easy, even more than I would have expected...