RIAA equalization - Wikipedia, the free encyclopedia for an explanation. On playback, the signal from a turntable must be amplified and re-equalized or it will sound much like you described.
What did you plug the leads from your turntable to? If your receiver is capable of accepting the signal from a turntable, you will find a pair of RCA jacks labeled "Phono". Does your receiver have such inputs? If not, you must buy a stand-alone phono pre-amp. It will amplify to the signal and apply the standard RIAA playback equalization. With a phono preamp, you can use any unused RCA jacks.
There are many such phono preamps available, and they do not have to cost a lot. Here is a good selection.