كتب : Omar AbdelAziz
The Blues, who largely relied on their 3-1 first-leg win last week, overcame a rampant Liverpool side as they hit four past Pepe Reina after the break.
Hiddink admitted that he had to go hard on his star-studded team at the break, following a poor start.
"Sometimes you lose your temper. But they reacted and they knew the first half was not OK," the Dutchman said after the game.
"We were angry because we didn't start as we planned and we know Liverpool are a good team tactically with very skilful players.
"Tactically but also mentally we said to each other, that it was not the way we would start the second half. That's why I like to work with this team, it reacts."
Proud
Despite the exit, Liverpool boss Rafa Benitez was elated with the performance of his side, who dearly missed influential skipper Steven Gerrard.
"We showed character, quality and we have to be really proud," said Benitez.
"The players have done a fantastic job and the fans will be very pleased with the team.
"We are not happy with the result. When you lose you are disappointed but to lose in this way, the players have to be really proud and hold their heads up high."
Liverpool saw their European campaign end at Stamford Bridge for the second season running, following last term's 4-3 aggregate defeat.