Shell functions cannot be trully embedded into Perl code. There are several reasons why your code does not work:

1. Function definition must contain parentheses in a shell.
2. There is a missing do after the for.
3. There is a missing semicolon after the first backquotes.
4. The main problem: each backquotes are run in a separate subshell. You cannot define a function in one subshell and run it in a different one (if it is not its subshell).

You can store the definition in a Perl variable, though, and prepend it to any code that needs to use it (note that backquotes interpolate variables):

my $f = 'forloop () {
for ((a=1;a<=5;a++)) ; do
  var="$a"
  echo "$var"
done
}';

my $result=`$f; forloop`;
print $result;
[download]

Nevertheless, usually implementing the whole logic in Perl might get you the clearest code.