Perl 6 wasn't the main factor. In the early/mid-2000s Perl lost mindshare because it's PHP equivalent - HTML::Mason - relied on mod_perl which cheap hosts were reluctant to offer for many reasons. Perl's main web framework, Catalyst, was a beast and only a few big companies took it seriously. There was also Mojolicious and Dancer but they never hit the big-time either.

Internally the Perl community fought with each other over how to implement OO. A Meta Object Protocal (MOP) was hotly debtated but the main implementation remained just a library. Likewise with Perl's main OO library Moose which spawned lightweight offspring such as Moo. TIMTOWTDI became a liability as competing scripting languages with built-in OOP (Ruby, Python & PHP5) ate Perl's lunch.

Perl also lost a lot of mindshare to Python in the an area it had dominated for many years - system administration.