You didn't get screwed by a password manager, you got screwed by a bad backup policy..
Sorry to be pedantic - and I feel your pain for losing your data - but there you go..
It also _probably_ means having these online somewhere. You're relying on strong crypto (and a really good base password) to protect you here.
If there was key-logging software on your machine, you're pooched any way you slice it (since such malware can just snarf decrypted keystores out of memory anyhow). However, with LastPass you can use Google Authenticator or a Yubikey or similar to enforce second-factor logins, so that even if you have malware on your machine, there is a drastically-smaller window in which to attack you.
On the upside, you get phishing protection (LP won't fill passwords for sites that don't actually match the site that you've saved passwords against), password duplication detection and strength auditing, notifications of when your passwords may have been compromised by major breaches, secure transport of passwords to other people, and transparent synchronization across devices. It's quite good.