We explore the role of disorder-induced localization in the dynamics of glasses and supercooled liquids using instantaneous normal mode (INM) analysis. This study is motivated by the fact that such localized excitations (tunnelling states and soft harmonic vibrations) are believed to be important in the thermodynamics and dynamics of amorphous systems at very low temperatures. The results are presented for two simple model systems that show the existence of a temperature below which all unstable INMs become localized. The relationship of this temperature to the glass transition is discussed.