That's a common mistake. I used make the same mistake myself. Don't panic! Tk::pack isn't broken.

Many widgets (including Tk::Label) have an -anchor option (see Tk::options). This option anchors the contents of the widget - typically text or an image. This is what you should be using, i.e. Label(-text => $text, -anchor => 'nw').

Tk::pack also has an -anchor option. pack() operates on the widget as a whole - it doesn't affect the contents of the widget. If, after normal packing, there's was free space to the north-west of the widget, pack(-anchor => 'nw') would move the entire widget in that direction. That's a simplistic description: read the full documentation for details of allocation rectangles, cavities and the packer algorithm.

#!/usr/bin/perl 

use strict;
use warnings;
use Tk;
use Tk::Pane;

my $mw = MainWindow->new();
$mw->geometry("100x100");
$mw->Button( -text => "START", -command => \&start_computation )->pack
+;

MainLoop;

sub start_computation {
    my $progress = $mw->Toplevel();
    $progress->geometry("100x100");
    my $pane = $progress->Scrolled(
        'Pane',
        -scrollbars => 'soe',
        -sticky     => 'we',
        -gridded    => 'y'
    )->pack( -fill => 'both', -expand => 1 );
    my $text = "Computation started...\n";
    $pane->Frame;
    my $label =
      $pane->Label( -text => $text )->pack( -side => 'left', -fill => 
+'x' );

    # doing several computation steps
    foreach my $step ( 1 .. 10 ) {
        sleep(1);
        $text .= "Step $step finished.\n";
        $label->destroy;
        $label = $pane->Label( -text => $text )->pack( -side => 'left'
+ );
        $pane->update;
    }

    $text .= "\nComputation finished.\n";
    $label->destroy;
    $label = $pane->Label( -text => $text )->pack( -side => 'left' );
    $pane->update;

    $pane->Button( -text => "QUIT", -command => sub { exit; } )->pack;
}
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There is no need to create/destroy labels, this is how you should write that

#!/usr/bin/perl --
use strict;
use warnings;

use Tk;
use Tk::Pane;

my $mw = MainWindow->new();
$mw->geometry("100x100");
$mw->Button( -text => "START", -command => \&start_computation )->pack
+;

MainLoop;

sub start_computation {
    my $progress = $mw->Toplevel();
    $progress->geometry("100x100");
    my $pane = $progress->Scrolled(
        'Pane',
        -scrollbars => 'osoe',
        -background => 'red',
      )->pack(
        -fill   => 'both',
        -expand => 'yes',
      );
    my $text = "Computation started...\n";
    my $label = $pane->Label(
        -textvariable => \$text,
    )->pack(
        -side => 'right',
    );

# doing several computation steps
    for my $step ( 1 .. 10 ) {
        sleep(1);
        $text .= "Step $step finished.\n";
        $pane->update;
    }

    $text .= "\nComputation finished.\n";
    $pane->update;
    $pane->Button( -text => "QUIT", -command => sub { exit; } )->pack(
        -anchor => 'nw',
    );
    return;
} ## end sub start_computation
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