The caretaker boss watched his side drop to the bottom of the Championship with a 4-2 defeat at home to Stoke, who leapfrogged them into 23rd place.
Barnsley do not play again until November 23 due to the international break, and caretaker boss Murray’s own position remains up in the air.
“It’s up to the board to decide,” said Murray of the prevailing uncertainty.
“We need a little bit of clarity now; for me it doesn’t matter either way.
“I think the players need that clarity when they return (from the international break), and then we can set targets for the rest of the season."
Murray’s chances of keeping the job will not have been helped by a demoralising defeat to a Stoke side who rallied under new manager Michael O’Neill.
Two goals from Sam Clucas, a penalty from Lee Gregory and a strike from Joe Allen capped a great day for the visitors, backed by around 2,600 fans.
Cameron McGeehan reduced the deficit to 2-1 in the 47th minute, and substitute Patrick Schmidt scored his first goal for the Barnsley two minutes after coming on as a substitute, which completed the scoring in a game that became progressively open.
“If you were doing a summary of our season, that (game) would be it,” said Murray.
“We made too many errors. The goals we conceded were individuals errors and that’s the story of our season so far.
“It goes past frustrating and you get a little bit angry with it.
“I know the fans do and the players do, and it’s something I’ve said to the players - we’ve got to start taking responsibility.
“There are no excuses.
"It’s time to stand up.”