Part of this is unavoidable because many mods add such shiny new things to look at. You will always have lower FPS on modded than on vanilla.
You can attempt to use Optifine (see stickie in this forum concerning how to do so properly). It might work, or it might not, but it lets you tweak a lot more graphics settings so you might be able to get it to run properly.
It sounds like you've got a bit of an older system, since you only had 22 FPS on vanilla. You might want to consider a more lightweight pack than the one you are trying to run.