You'll need to version 0.40 for this to work:

use Template::Extract;

my $template = <<'EOD';
[% FOR records %]
[% ... %]
 OAMPG: [% oampg %]   Extent ID [% extent_id %] on allocation page [% 
+alloc_pg =~ /(\d+)/%]
[% END %]
EOD

my $doc = <<EOD;
 OAMPG: 600   Extent ID 608 on allocation page 512
 OAMPG: 128   Extent ID 616 on allocation page 512
EOD

use Data::Dump::Streamer;
Dump(Template::Extract->new->extract($template, $doc));
[download]

I'm not sure what the exact problem is with Template::Extract but I suspect it is because it needs a trailing token for the match to halt.