Mitrovic, 21, is currently the club's only fit orthodox striker and he has just three goals to his name this season.
McClaren said: "It's not rocket science, is it? To win games of football, you have to score goals and at the present moment, we have to score two to win games because we are conceding one every game.
"It doesn't matter how old you are, strikers want to score goals. They're the worst people in the world when they're not. But Mitro's working damn hard out there, and we continue working and he will.
"I'd be more worried if we weren't working because it's not just his responsibility. It's [Moussa] Sissoko's responsibility, it's [Georginio] Wijnaldum's responsibility, [Ayoze] Perez's responsibility, [Florian] Thauvin, Siem de Jong, Papiss.
"It's everybody's responsibility, not just the number nine."