#!/usr/bin/perl
use warnings;
use strict;

my $line = '|Match_regex_1a_P_a|Match_regex_2_a|Match_regex_1b_P_b|Mat
+ch_regex_2_b|';

my $regex1 = qr/\|(?<DataCapture>[^|]+)_P_/;
my $regex2 = qr/\|(?<DataCapture>(?![^|]+_P_)[^|]+)/;

use Test::More;

my @matches1 = map "Match_regex_1$_", qw( a b );
while ($line =~ /$regex1/g) {
    is $+{DataCapture}, shift @matches1;
}

my @matches2 = map "Match_regex_2_$_", qw( a b );
while ($line =~ /$regex2/g) {
    is $+{DataCapture}, shift @matches2;
}

done_testing();
[download]

Where

[^|]+_P_
[download]

matches exactly what you want to avoid.