Have you looked at this? Regular Expressions in Calc
Ignore the differences--they're beside the point. The parentheses are only needed if you're using Find & Replace, so I left them out. Robert's regex would work just the same if you used it in the SEARCH example.
Walk through it one element at a time:
\\ A single, literal backslash character. You have to use two in a row because the backslash is a special character in regular expressions; two in a row means a plain, non-special backslash character.
[^\\] A class (or set) of characters, any of which will count as a match. In this case, the set has only one character, our literal backslash friend again. The caret ^ causes the meaning of the set to be inverted: instead of matching any character in the class, it matches any character not in the class. So this means: "match any character other than a backslash".
* This is a repetition marker; it means the preceding pattern element should match zero or more times. So that's any character other than a backslash, any number of times, including none at all.
$ This matches only at the end of the input.
So all together, it matches a backslash, followed by any number of non-backslashes, followed by the end of the input. That's a long way of saying "the last backslash in the input".