In your simple case of printing several values with a constant separator, there's either join, or $,:

print "Values: ", join ", ", $self->get_value1, $self->get_value2, $se
+lf->get_value3";
print "\nValues: ";
{
  local $, = ", ";
  print $self->get_value1, $self->get_value2, $self->get_value3"; 
  print "\nValues: ".$self->get_value1, $self->get_value2, $self->get_
+value3"; # notice the . after "\nValues: "
}
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All three of those solutions have their downside though.

For the most general case of printing method calls inside double quotes, all I can think of is using a tied hash to call the methods when accessing it. It works but it kind of defeats the purpose of writing accessor methods in the first place:

use v5.14;
use strict;
use warnings;

package Test {
  sub new { my $scalar = $_[1]; bless \$scalar, shift }
  sub value { ${ $_[0] } = $_[1] if @_ > 1; ${ $_[0] } }
}

package CallerHash {
  sub TIEHASH {
    return bless \$_[1], $_[0];
  }

  sub FETCH {
    my $obj = ${ +shift };
    my $method = shift;
    return $obj->$method();
  }

  sub STORE {
    my $obj = ${ +shift };
    my $method = shift;
    $obj->$method(@_);
  }
}

my $obj = Test->new(4);

tie my %objAsHash, CallerHash => $obj;

say "$objAsHash{value}";
$objAsHash{value} = 42;
say "$objAsHash{value}";

say $$obj;
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Edit: BTW, the fact that $method = "method_name"; $obj->$method(); works even under strict might help you come up with another solution to print the output of method calls without concatenating bits of strings. Maybe something like: print replace $self, "Values: {self:get_value1}, {self:get_value2}, {self:get_value3}"; where replace uses s///ge;
(so now that I think of it, the tied hash isn't the only solution I can come up with)

Edit2: haukex is right. Using a templating engine is probably the best idea