Pieters was named in Burnley's starting line-up despite being suspended after receiving bookings in the previous two rounds of the competition.
And Dyche says Burnley were informed of their 'administrative error' by Bournemouth's head of media and communications, Anthony Marshall.
He said: "It wasn't disruptive. It was just a simple admin error. We have people who keep an eye on situations, unfortunately it got away from that moment where someone found clarity.
"The rules have changed this year with the booking situation and the number of games in the FA Cup. It was just a clear oversight.
"To be fair to Bournemouth, they flagged it and mentioned it, so credit to them for a bit of gentlemanly conduct. We jumped on it straight away and people at our club held their hands up in the right slots."
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