Wednesday produced 22 attempts on goal with eight on target against the Stags, but had just one goal to show for it, by way of Anthony Musaba's first goal of his Owls career.
League Two outfit Mansfield, enthused by Wednesday's inability to kill the tie off, came back into the game late on and took the match to a penalty shoot-out, thanks to Rhys Oates's late goal.
Mansfield held their nerve on spot-kicks to win 5-4, with subs Will Vaulks and Liam Palmer missing for Wednesday, who visit Elland Road on Saturday.
Looking ahead to that Yorkshire derby, Munoz said: "The players have experience, responsibility and they need to know if they can give better or not.
"I try to always give my best and the important things - and after we will see what happens against Leeds. It's a big challenge.
"It is a better team than us, but 100 per cent we will go there and try to give (get) the three points.
"I think everybody knows to give something more, we have responsibility to our club and our team and fans. Everybody needs to give 100 per cent."
Bemoaning his side's lack of killer instinct in a game they should have won comfortably, he continued: "This is the difference. If we improve and score again, then we kill the game.
"We had three or four important chances against Cardiff and after the game, it kills you. It is the capacity we don't have at the moment.
"We played a very good game (against Mansfield), but in the last third, we need something special.
"They shoot maybe five times at most? And score. We shoot 25 times and we are the team from the Championship, they are League Two.
"We shot 25 times, but when you don't score, this is football. If you give them chance to shoot - we have to reflect and everybody is thinking about how we change this situation.
"It's impossible to lose this game... Another individual mistake led to it (Mansfield's goal)."