The Clarets go to Moyes' West Ham on Sunday.
Konpany said: "I think he has always done well.
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"He's won a European trophy - what more do you have to say? What could crown the job that you've done at a place better than that?
"I'm not surprised (he gets criticism). I wish for him to win another European trophy - I guess that will settle it. From my side, I can just speak about what I've seen him do over the years. That's also the reason why it's a great manager to come up against and a great game for us to look forward to."