Cousin is still waiting on a move to Fulham and Burke said: "Daniel is happy here and, as a player he wants to play well as soon as he steps onto the pitch no matter who he is playing for.
"So I do feel for him and I just ask the fans to get behind him.
"He is stepping onto that pitch for Rangers, and if the fans get behind him it will encourage him and make him play better.
"We don't want to see any our team mates getting flak. We play as a team and we want each other to do well and we work hard for each other."