The Chilean guided Real to a 3-2 comeback win over Sevilla in the league to put them ahead of Barcelona for the first time in weeks but that may be quickly forgotten if they do not overturn a 1-0 deficit at home to Olympique Lyon in the Champions League last-16 on Wednesday.
After spending around 250 million euros on new players in the close season, it is success in Europe that matters more than ever at Real, especially given that they have fallen at this stage of the competition for the last five years.
"We recognise the Champions League holds a special importance for this club," forward Cristiano Ronaldo told a news conference on Monday.
"They have won it nine times and want to win it a 10th time. The final is being played here at the Bernabeu, but we have to take it game by game.
"Obviously, it would be a big disappointment if we didn't progress, but I am sure we will."
He told reporters recently: "Real love the Champions League above all else. The club has the word 'Europe' in its DNA."
"We need to go out with the mentality that we are going to win, to score goals, and if it is with a more offensive midfield all the better. But that's the coach's choice," the Portuguese said.
Pellegrini has still to convince many observers, with newspaper Marca writing after the win over Sevilla: "Pellegrini has a rare ability. He doesn't make good decisions, he rectifies previous ones."
One thing he can rely on though is Real's firepower, and his team have responded to the defeat in Lyon by rattling in 14 goals in the three matches since then.
The visitors have never beaten one of Europe's top sides in the knockout stages but will prove tough opponents.
"We really believe in our chances, even if Real remain the favourites," Lyon captain Cris, told reporters.
"It's just a match with 22 men and we are not worried about their stars. All we have to do is be strong in our heads."
