Don't use a regex, use File::Spec, which is a core module (or you can use e.g. Path::Class or Path::Tiny from CPAN). use File::Spec; my $filename = File::Spec->splitpath($fullpath); - if this script is running on a non-Windows system but you need to handle Windows filenames, write File::Spec::Win32 instead of File::Spec.
Update: After rereading I realize you're also trying to extract the path from a string that looks like "TEXT: \"...\"". I feel like we might be missing some context, because the file format is unclear to me - is this some standardized file format you're trying to extract a part of? If so, what format? Usually quoted strings also have some kind of escaping mechanism, is that the case here? All of this things will affect what the best solution is. If the format really is as simple as it seems, then I would combine Corion's solution to extract the string from the quotes with my suggestion above to extract the filename.