Perhaps you have a good reason for eschewing use of a module, but comments like "I am trying to do it in regex and not use a specific module." are often ill-founded unless rooted in exercising/expanding your knowledge.

Nonetheless, split and a regex will do the job (for your limited sample data):

use warnings;
use strict;

# 737495

my $text = ' example.txt "unimportant1" "unimportant2" "unimportant3" 
+"time" "data1" "data2" ';
my @words = split/ /,$text;

for my $word(@words) {
    if ( $word =~ /(data)(\d)/ ) {
      print "Data" . $2 . ": $1$2 ";
    }
}


=head Execution:

perl 737495.pl
Data1: data1 Data2: data2

=cut
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