Every footballer missed a 10 yards pass. Is that mental toughness? Or just an ability to do it 100% of the time.
Most people are affected by pressure to some degree. But ultimately pressure is something you put on yourself - if you feel that 80,00 people in the stands puts pressure on you, it does. If you're one of those random freaks who just thinks that those 80,000 people don't actually make a difference to the task you have to perform then you don't feel pressure.
"I don't feel pressure ... I don't give a toss about it. I spent the afternoon of Sunday, July 9, 2006 in Berlin sleeping and playing the PlayStation. In the evening, I went out and won the World Cup." - Andrea Pirlo
Sports psychologists try to make professionals perform their basic technical skills the same regardless of the situation. If we are having issues with missing penalties I'd say the problem is mental not technical.
You're actually agreeing with me though by saying it's easy to get nervous taking one at the park - that shows that the issue is largely mental.
I'm not saying that we should expect our players to feel no pressure at all, but that there are certain personality types that respond better in those situations. And, those psychological traits can be developed through things like breathing exercises, visualisation, etc