Eagles boss Burley said: "I have had a wee chat with the referee because I thought he had a poor performance. You put a report in and an assessor looks at it but it's too late then.
"I thought my team showed spirit and courage and a desire to get something out of it and there were some very encouraging signs.
"But a decision where the lad (Evans) is three yards offside for their equaliser (at 2-2) cost us.
"I'm really disappointed for the team because they put in so much effort, playing with 10 men for most of the game.
"When you look at their first penalty and then the offside goal, they were key to the game."
Regarding Garvan's dismissal, Burley added: "It was never a penalty and out of frustration he swore."
It was only United's third home win of the season, and their first since September 18, and moved them up to 18th with Palace remaining second bottom.
Sheffield United boss Gary Speed praised his team's character.
"I said it would be difficult to play against 10 men and that's how it proved to be," he said.
"Palace defended great and made it difficult for us to break them down, but we showed our desire to come back.
"I thought both penalties in the first half were dubious. I think the referee knew he made a mistake with their penalty and he gave us one to even it up.
"I think the penalty he gave us for the winner was the only definite penalty of the night.
"The defending for their second goal was poor and that's what I'd warned them about at half-time. I told the players to be disciplined out of possession.
"Speroni (Julian, Crystal Palace keeper) made some good saves but the important thing was that the players didn't get anxious. They showed character and desire to come back and get a result."
Speaking about Bogdanovic's sending-off, Speed added: "He scraped down his leg and I understand why the referee sent him off - because that's the way the game is now - but there's no malice in him whatsoever.
"'Boggy' hasn't even made a foul in training yet."