When a team suffers a defeat, especially a huge one, the defeats can affect them in two different ways: it can make some loose confidence in themselves and result in them losing more games, or it can make a team more determined to change the results in your next game. For Nottingham Forest, the defeat they experienced pulled them together. They deserved the win.
Liverpool were also able to make sure to stop Bournemouth's run of form. Not an easy win, but an important one to make sure they maintain their advantage.