It is has not been replaced by nothing. What has been taken away, without replacement, is the feature to write use encoding 'ISO-8859-5'; and then use cyrillic characters in that encoding in character literals of your source code. But you didn't do that, you declared UTF-8, and there is a replacement for that:
There is use utf8; which is the equivalent of use encoding 'utf8';
Note that (precisely: Since Perl 5.8.2) neither of those affects how your program reads and writes text: They are used to declare that your source code is encoded as UTF-8. So it mostly affects string literals in your code, but not templates or anything else your program reads or prints to.
If you want to set a default encoding, have a look at open. If you write use open ':encoding(UTF-8)'; then every calls to open within the lexical scope of the open pragma will be UTF-8 encoded.