I seen that $mw->idletasks; takes the effect. In this case, You getting the status once you pressed the button. There are sometimes or in some places, we require the status to be updated once we pressed the enter key. For this, the following would help,

my $input = $mw->Entry(-takefocus => 1,
    -textvariable => \$upper_no,
    -width => 12)
    ->place(-relx => 0.50, -rely => 0.05);

my $counter_label = $mw->Label(-textvariable => \$no,
     -relief => 'sunken',
    -anchor => 'center')
    ->place(-relx =>0.0, -rely => 0.80, -relwidth => 1.0, -relheight =
+> 0.2);

# When <enter> is pressed, this taken into the action.
$input->bind('<KeyPress-Return>', sub {
                count();
                $counter_label->configure(-textvariable => \$no);
            }
        );
[download]

This might helps for you.