The Huns came in and started forcing barbarian tribes west which resulted in some tribes going into the Roman Empire and when the Romans did not provide food for the tribes that immigrated there, they turned to rampaging. Some barbarians had to go elsewhere after having to leave their homes.
The barbarians played a role in the Roman Empire falling, but they are not the only cause. Other reasons for failure include a failing economy, splitting the empire in two, high taxes and the soldiers being more loyal to military leaders than the emperor. The intolerance of Christians is also important because they did not tolerate other religions and cultures.