my $count=($str2=~ tr/$t1//);

This will count how often the characters in $t1 are in $str2 ...

Unfortunately, the  tr/// operator does not interpolate, but the  s/// or, better yet, the  m// operator can serve here:

>perl -wMstrict -le
"my $s = 'foo bar fooo bar foooo bar';
 my $cc = 'foz';
 ;;
 my $count = ($s =~ tr/$cc//);
 print $count;
 ;;
 $count = '$c$c$' =~ tr/$cc//;
 print $count;
 ;;
 $count = $s =~ tr/foz//;
 print $count;
 ;;
 $count = $s =~ s{ ([$cc]) }{$1}xmsg;
 print $count;
 ;;
 $count =()= $s =~ m{ [$cc] }xmsg;
 print $count;
 ;;
 $count = $s =~ s{ [$cc] }{}xmsg;
 print $count;
 print qq{'$s'};
"
0
5
12
12
12
12
' bar  bar  bar'
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Note: There is no need for a capture group in the  s/// expression if characters in the string can be counted 'destructively':
    $count = $s =~ s{ [$cc] }{}xmsg;

Update: Added  s/// and  m// examples, discussion.