I'm guessing somewhat regarding what you want to achieve.

Always put strict and warnings at the top of your code. In this instance, that would have alerted you to the fact that there was something wrong with $f.

I was unsure why you wanted to increment $i inside the loop. In my version, I changed $i+=2 to $i+2.

Here's a couple of ways of doing what I think you want:

#!/usr/bin/env perl

use strict;
use warnings;

my @f;

# Modification of your code
for my $i (0..2) {
    my @e = ($i+2, $i+1);
    push @f, [@e];
}

# A more succinct way to achieve it
for my $i (3..5) {
     push @f, [$i+2, $i+1];
}

# For demo purposes
use Data::Dump;
dd \@f;
[download]

Output:

[[2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6]]
[download]

See also: "perlintro: Arrays"; "perldsc - Perl Data Structures Cookbook"; "perllol - Manipulating Arrays of Arrays in Perl".