Former Real striker Huntelaar's return to the Santiago Bernabeu proved a fruitful one as he scored twice in Tuesday's last 16 second leg, including a stunning 85th-minute effort that set up a frantic finale.
However, Schalke - who were defeated 2-0 in the first leg in Gelsenkirchen - ultimately fell short and Huntelaar believes the team's inability to twice hold onto the lead before half-time was the decisive factor.
"Of course we are happy about our game, but we could have achieved more," he said.
"We conceded too easily and we should have taken our lead into the break. They didn't feel comfortable at all."
Real's latest blip was met with a chorus of whistles by the home supporters as they failed to hold onto to the lead despite Karim Benzema putting them ahead in the 53rd minute.
And Schalke captain Benedikt Howedes felt Roberto Di Matteo's side deserved more for their efforts.
"We played a great game. We were very brave and haven't been outshone by a world-class team like Real Madrid," he said.
"Congratulations to my team. We deserved more."
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