I'm having some trouble with pull offs. I have been making a conscious effort to kind of flick the string when pulling off a note, but when I do this on the lower strings, it bends the note slightly and doesn't sound right, even when I practice really slowly. I don't want to blame my strings, but they're .11s in D standard if that makes a difference.

How should I fix my problem?
Sounds like your being a little too hard on the string. You may be pulling the note out of tune before releasing. I just lightly flick and at the same time pull my finger up.

I also use .011's in D standard, and I think they work pretty well for that tuning. just try a gentler touch and see if that helps. It takes a long time to develop good legato technique.
Yep, you're probably flicking too much "down" when it's actually "out" from the fretboard as much as down. Don't forget that you need to have a little pressure on the finger you're pull off to if you're going to flick that hard.