How do I say \"is not\" a certain character in sed?
There are two possible interpretations of your question. Like others have already pointed out, [^x] matches a single character which is not x. But an empty string also isn't x, so perhaps you are looking for [^x]\|^$.
Neither of these answers extend to multi-character sequences, which is usually what people are looking for. You could painstakingly build something like
[^s]\|s\($\|[^t]\|t\($\|[^r]\)\)\)
to compose a regular expression which doesn't match str, but a much more straightforward solution in sed is to delete any line which does match str, then keep the rest;
sed '/str/d' file
Perl 5 introduced a much richer regex engine, which is hence standard in Java, PHP, Python, etc. Because Perl helpfully supports a subset of sed syntax, you could probably convert a simple sed script to Perl to get to use a useful feature from this extended regex dialect, such as negative assertions:
perl -pe 's/(?:(?!str).)+/not/' file
will replace a string which is not str with not. The (?:...) is a non-capturing group (unlike in many sed dialects, an unescaped parenthesis is a metacharacter in Perl) and (?!str) is a negative assertion; the text immediately after this position in the string mustn't be str in order for the regex to match. The + repeats this pattern until it fails to match. Notice how the assertion needs to be true at every position in the match, so we match one character at a time with . (newbies often get this wrong, and erroneously only assert at e.g. the beginning of a longer pattern, which could however match str somewhere within, leading to a "leak").