As haukex has already pointed out, it's probably best to avoid eval in this case as it could be manipulated to run arbitary Perl code in your example.

hippo has also made a valid suggestion about using the ternary if conditional to make the code easier to read.

Personally, I'd use both of these suggestions, add in the use of say rather than print when appropriate and move the display prompt and return input into a separate function, but that might be over-engineering this learning exercise.

Putting it all together gives the following:

use strict;
use warnings;
use 5.016;

sub prompt_read {
    print shift;
    chomp( $_ = <STDIN> );
    return $_;
}

say "RegEx Engine 1.0\n________________";
my $str     = prompt_read("Gimme a string: ");
my $pattern = prompt_read("Gimme a RegEx: ");
say $str =~ /$pattern/ ? "Yes!" : "No!";
say "kthxbye";
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