Former Tottenham and Hull midfielder Marney received his marching orders for a tackle on Blues defender Paul Robinson shortly after the hour.
The match was poised at 1-1 at that stage before Marlon King fired home a last-minute winner for the visitors.
Having considered referee Darren Drysdale's decision over the weekend, Clarets boss Sean Dyche confirmed his desire to have Marney's prospective three-match ban quashed.
"We will be appealing," he said in a club statement. "We felt it was the wrong decision at the time and since then we have looked at the incident again in the cold light of day to confirm our belief.
"We've also sought a few opinions from other people that confirm our thoughts, so we will put our faith in the appeals process in the belief we can get the right outcome and have the red card rescinded."
Meanwhile, Burnley's home league game against Hull has been moved back two days to Monday, March 11 for live television coverage.
- Sports & Recreation
- Marlon King