The Mexico international moved to the Santiago Bernabeu on a season-long loan after finding starts hard to come by at Manchester United.
However, Hernandez's opportunities in the first-choice XI have proved just as limited at Real and he has started just once in La Liga this term.
Real coach Carlo Ancelotti afforded the 26-year-old striker a chance to shine the Copa, though, and he responded with Real's goal at the Estadio Municipal de la Via Ferrea.
And Hernandez is keen to show his value to the team.
"I'm working hard to seize opportunities and do my best for the Madrid badge," he told reporters after the game.
"I won't get into this debate [about being a substitute]. I'll prove my quality when I'm playing."
Real's fourth goal was scored by substitute Marcelo, with the full-back celebrating with a double somersault.
And the Brazilian's exuberant reaction was frowned upon by Cornella goalscorer Oscar Munoz.
"We are Segunda B players, we hardly earn any money and his somersaults leave a bitter taste in our mouths," he told Marca.
"You have to remember where you are. Well, whatever - after he told me that he just had to celebrate it. Chicharito [Hernandez] also explained it to me. He told me that he doesn't score all that many goals and that's why he did it."