Still reeling from their humiliating 5-1 defeat at Barca last week, Real made an impressive start against a Real Valladolid side unbeaten in their last six outings.
Saturday's game is the first of three tests for Solari before the next global break and a home win against Valladolid followed by two victories on the road against Viktoria Plzen and Celta Vigo would probably be enough to convince club President Florentino Perez to hand Solari the job, rather than go for a big-name replacement such as Antonio Conte.
"We have to lift ourselves up, we understand the fans' frustrations and why they are booing".
Gareth Bale, Casemiro and Benzema all went close with headers, two of them swung in from 21-year-old left-back Sergio Reguilon but Valladolid survived.
Wayne Rooney to make England comeback
At the time the 33-year-old announced his decision to retire in a low-key statement. I hope that whilst I am with the squad I can pass on some of my experience.
Real Madrid captain Ramos has now responded to the treatment he received from fans during the game.
Clearly blessed with fine crossing ability, young Madrid defender Reguilon was a threat going forward and never less than assured defensively as he repaid the faith of long-time Castilla coach Solari.
"My pride is what has got me where I am today, and beating all the records I have beaten".
"When the ball won't go in you have to keep calm", Ramos said.
"It was a hard occasion because of the run we've been in and changing coach", Ramos said. "There are moments when you have to have order, commitment, a serious attitude, effort and a competitive spirit, and we showed those tonight and we won".