Spock said that the gravity systems were failing, that could mean they were going haywire, it didn't help that the Enterprise was caught in the gravity field of Earth.
The Enterprise is 267,000km from Earth when she drops out of warp, the moon is 384,405km away. The Enterprise is 117,405km closer to the Earth. The pull is stronger.
Don't claim shit science when you didn't even take 10 seconds to find that out.