Others have mentioned binary search in case your array is sorted. If your array is not sorted, you'll have to scan over the whole thing. Here's a short way to do this that makes the intent obvious:

use List::Util 'max';
my $selected = max grep { $find >= $_ } @array;
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That's somewhat inefficient, however, because it actually loops twice (once for the grep and again over whatever grep produces).

You could write it in one loop this way:

# Find the largest number in @array
# that is <= $find and put it in $selected
my $selected;
foreach my $number ( @array ) {
    $selected = $number    if $find   >= $number
                          and $number >  $selected;
    last if defined $selected and $selected == $find;
}
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If you're not going to have a huge list, there's little downside to doing it the easy way. (In fact, for short lists, I wouldn't be surprised if the grep method is faster.) If you do decide to write your own loop, be sure to comment it, and maybe put it off in a sub with a good name.