Liverpool, trailing 3-1 from the first leg, almost pulled off another sensational European comeback as they raced into a two-goal half-time lead through Fabio Aurelio and Xabi Alonso (penalty).
But Hiddink's verbal volley saw Chelsea score three times thanks to Didier Drogba's goal courtesy of a Pepe Reina error, a free-kick from Alex and a clinical finish from Frank Lampard.
It put Chelsea 6-3 ahead on aggregate but astonishingly Liverpool hit back with two goals in as many minutes from Lucas and Dirk Kuyt before Lampard's second killed off their hopes of achieving the unthinkable.
But Hiddink ensured Chelsea went out for the second-half with his words ringing in their ears.
"We talked to them, my colleagues talked to them and sometimes you lose a bit of your temper," admitted Hiddink.
"But they react and they also knew the first half was not okay.
"But if you give a team like Liverpool too much space then you are in trouble.
"We were angry because we didn't start as we planned and we know Liverpool are a good team tactically with very skilful players.
"You cannot give them a lot of space but we did. We dropped back too much and looked for safety.
"The focus is also on the duels. We lost too many of them in the first half and that was not good.
"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.
"We knew that we could score and happily we did rather early after the beginning of the second half.
"But you cannot stay angry because then the anger becomes frustration.
"But this was one of those games where players have made a lot of errors. That's why it was very attractive - going from one goal to the other.
"It was very dramatic. One moment you think you are down and then the team reacts and then you are up before you are down again. It was a wave of being in the game then almost being out of it.
"It is exciting but you suffer a lot when you are responsible. When it is paying off as it did tonight it is good to be involved for many, many years, but we know the situation."
Hiddink admitted that goalkeeper Petr Cech is not on top of his game but refused to think about dropping him.
Cech looked out of sorts as Bolton scored three goals in nine minutes last Saturday and he looked shaky again against Liverpool.
He was hopelessly out of position for Aurelio's opening free-kick and looked out of sorts all evening.
"He is a very intelligent and self-critical goalkeeper," said Hiddink.
"He was not happy with his performance against Bolton although there was always a sequence of errors before he came into action. But he is very critical of his own performance even when he has had an almost perfect game.
"There were some things tonight where you could see he was not full of confidence. I think a goalkeeper once in a while has a right not to have a big performance.
"But he will stay a very good goalkeeper, every person sometimes has this small period of not being on top form. If a player is playing a lesser game now and then, it is not always the reason to make a substitution."
Chelsea now face Barcelona in the semi-finals and will have to do without a recognised left-back in the club.
Wayne Bridge was sold to Manchester City in January, Paulo Ferreira is injured and Ashley Cole will be suspended for the first leg in Spain after picking up a booking.
"The left-back situation might cause problems but we have time to think how we might resolve it," said Hiddink.
"Barcelona are a very advanced team with very skilful players. They know how to handle the pace. I like their philosophy of football.
"They sign players who are attractive to watch. They like to play advanced attacking football and it is difficult to play them because they are a top side."
Liverpool coach Rafa Benitez was immensely proud of his players after they almost achieved another sensational European fightback.
After an emotional week on Merseyside because of the 20th anniversary of the Hillsborough disaster, Benitez insisted the performance would have pleased the fans.
"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 were on top of them from the beginning and doing a fantastic job. It is a credit to all the players, especially Lucas in the middle in the position of Steven Gerrard - he worked very hard.
"Thanks to them we were pushing and were very close. But when you play against a good team like Chelsea, if you make a mistake you pay for them.
"We were attacking and controlling but one or two mistakes allowed them to score.
"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."
Benitez believes that the result could be the springboard for a final push for the Barclays League title.
"Maybe it is a positive because we saw we can score four goals here and we can do the same in any stadium. We can win a lot of games with this mentality."
Gerrard's absence was more crucial than ever but Benitez said there was never any prospect of him playing after last night's training session.
"He felt something, so he was unavailable," said Benitez. "We thought he could be okay but in the end he felt something. It was an easy decision because he could not play.
"To lose a key player is always important and especially a player like Gerrard but credit to the other players because they did a fantastic job.
"It is not serious and we felt he could be available but he wasn't. Hopefully it will be okay."