Seems to work for me ... what are you getting, and what are you expecting, for the sample log file you're showing?

#!/usr/bin/perl -w

use strict;
use warnings;

while (my $file_content = <DATA>) {
    if ( $file_content =~ m/Vc3/ ) {
        my @numbers = $file_content =~ /\[(\d+)\]/g;

        { local $,=':'; print @numbers; print $/ }
    }
}

__DATA__
            Item no.0:  NameDepth [2]

        <0>   Class: [1] NetElementObjectClass                Instance
+: (int) [2]
        <1>   Class: [ 57 ] Vc3TtpSnkObjectClass                Instan
+ce: (int) [3]
                Item no.1:  NameDepth [2]

        <0>   Class: [1] NetElementObjectClass                Instance
+: (int) [2]
        <1>   Class: [ 57 ] Vc3TtpSnkObjectClass                Instan
+ce: (int) [14]
[download]

gives me:

$ perl ./x.pl
3
14

Seems right to me - are you expecting to get the 57 as well? If so, you need to tell the regexp to ignore spaces:

        my @numbers = $file_content =~ /\[\s*(\d+)\s*\]/g;
[download]

Hope that helps.