Applaud students for the time spent playing. Reward them for it, not necessarily for their accuracy. It takes time to learn to critical analyze a task, especially for young children, they simply do not have that ability yet. But they do have the ability to learn to keep trying something even when it is hard. Music lessons help them learn that just because something is hard, does not mean it will always be hard. Keep trying and soon it will become easy- that's the magic of music!
Whenever my students tell me, "Ugh, this is hard! I can't do it" My response is always, "Yet. You can't do it yet." And then we talk about a previous piece they mastered.
I say, "Remember when you thought Jingle Bells was too hard? Is it still hard now?"
And they always say, "No! Jingle Bells is soooo easy!"
"Well, if you keep trying then before you know it this piece will be easy too! It's like magic!"
I always talk kids through this process, because they get very frustrated with their own limitations, but with help, support, and encouragement they will get through it...and they will learn to apply that focus to other skills as well!