Interpolation rules for here-docs are the same as for double- and single-quoted strings (double in the OPed example), so one way:

c:\@Work\Perl>perl -wMstrict -le
"use constant OUT_SUFXSTOR => 'storable';
 ;;
 my $str = qq{The file suffix is ${ \ OUT_SUFXSTOR}.};
 print qq{'$str'};
"
'The file suffix is storable.'
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Update: Then there's also:

c:\@Work\Perl>perl -wMstrict -le
"use constant OUT_SUFXSTOR => 'storable';
 ;;
 my $str = qq{The file suffix is @{[ OUT_SUFXSTOR ]}.};
 print qq{'$str'};
"
'The file suffix is storable.'
[download]