Hernandez struck his first UEFA Champions League goal since November 2012 at the Santiago Bernabeu, tapping Cristiano Ronaldo's cross into Atletico's net with two minutes remaining in the quarter-final second leg.
It continued the 26-year-old's impressive recent run, as he started for the third time in Real's past four matches in all competitions - he was left out of the quarter-final first leg - for a return of two goals and one assist.
"My goal is for all of the people who always had faith in me - my team-mates and my family," Hernandez told the host broadcaster. My goal is dedicated to all of them."
After a tough few seasons - Hernandez has started just 18 league games for Manchester United and Real since the end of the 2011-12 season - the Mexico international was thrilled to make an impact on such a big stage.
When asked if his goal was the most important of his career, he replied: "Yes, of course because the present is what matters.
"I have scored other important goals in my career but the ones that count are the ones I score now. Tonight's goal will give me confidence. It was a great pass from Cristiano to set me up. It was our turn to win."
Hernandez is on loan from United to Real until the end of the 2014-15 campaign.
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