I know we're supposed to hate goto and never ever ever use it, but it does make for a very clear solution in this case:

#!/usr/bin/env perl
use Modern::Perl;

while(<DATA>){
    goto SKIPPED if /match/;
}

say 'Do something after normal loop exit';

SKIPPED:

say 'Proceeding with rest of program';

__DATA__
line 1
line 2
match line 3
line 4
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