Fellow midfielder Xabi Alonso believes it was the world champions' concentration rather than fatigue that betrayed them as they were hammered 5-1 by the Netherlands in their opening game.
Vicente del Bosque's men now almost certainly need to win their remaining two matches against Chile and Australia to avoid the humiliation of joining France and Italy as World Cup holders that crashed out at the group stage.
"In football every three or four days there is a game and the chance to put things right," said Fabregas.
"This team has character and courage. It is one of the most difficult moments in the past few years, but I believe a lot in this team."
Chelsea's new signing could start should Del Bosque ring the changes for Wednesday's clash with Chile in Rio.
And he says the players know just how important the next match is and insisted they will respond in the style of champions that have won their past three major international tournaments.
"We know what we are playing for. It is not a unique thing in football, there are times when given the necessity to score goals or the way the opponent plays you are obliged to attack and be brave," he said.
"We have players of very high quality and I don't know why we can't give a masterclass of football.
"We will give everything to win because that is the only option we have. From what I have seen, Chile will press high, they want to score goals and it will be a tightly contested game.
"We need to take advantage of the weaknesses they have too. It is a game of life or death for us, we have to win and that is what we will try to do."
Alonso said now was not a time to panic or make rash decisions but rather one for cool reflection.
"After a bad result against the Netherlands, we are analysing little by little what happened and thinking about all the things we have to correct," said the Real Madrid midfielder.
"But I believe in this group and that we have won the right, the credit to have this chance to redeem ourselves and turn the situation around.
"Chile play in a similar style, they have a very brave way of playing. They go for the opponent and are aggressive.
"We know them well and after the very bad result against the Netherlands we know that it is a final in which only a win will do for us.
"After it went 3-1 we tried to respond but more with our hearts than our head and we were disorganised.
"They scored two more goals, but it wasn't due to our physical condition, but the fact we didn't respond in the right way. They kept moving the ball and created plenty of spaces."