I'd probably simplify that a bit, with a possible (minor) speed benefit.

First, we should conceptualise how to approach the problem. As a human. (My experience with Perl is that it's even better than many other languages at doing what a human does, which improves both readability and reliability.) So, what I would do, as a human, would be to look for each letter in the target string, and if all of them are there, then I have a match. That "all" is a big clue - checking modules for such behaviour, I find it in List::MoreUtils. (Side note: since other monks have pointed me to List::MoreUtils, I've found more and more use for it, so much so that I'm now wishing it were core!)

The advantage, of course, of using such a tool is that it short-circuits your code (returning at the first failure rather than continuing), and, in this case, it's written in XS, so should be faster than a simple perl duplicate. In the worst case, where all letters are present (or all but the last letter), this should perform basically as well as yours (except I don't need to create a list to count it), and on average, it should perform better. However, that should all be pretty minimal - instead, the real benefit is doing what a human does exactly the same way. And that makes it more likely to work in weird circumstances.

So, after all that build-up, I had better show some code. Note that I've renamed the function because I like my boolean-returning functions to sound, well, boolean. "Check for letters" doesn't tell me what it returns (sounds like it doesn't have a return value, actually)...

#! /usr/bin/perl

use strict;
use warnings;

use List::MoreUtils qw(all);
sub hasAllLetters
{
    my ($sentence, $letters) = @_;

    # all we're doing is checking for each letter.
    all { $sentence =~ $_ } split //, $letters;

    # same as above, but with index which I think is less readable.
    #all { index($sentence, $_) >= $[ } split //, $letters;
}

# tests
for my $t (
        [ "abxcd zwe rrv", "zxv" ],
        [ "abxcd zwe rrv", "qxv" ],
       )
{
    if (hasAllLetters(@$t))
    {
        print "YES [$t->[0]] ~~ [$t->[1]]\n";
    }
    else
    {
        print "NO  [$t->[0]] !~ [$t->[1]]\n";
    }
}
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(If performance was really an issue, I'd not only benchmark it, but I'd use @_ directly instead of giving them readable names.)