The mood at the Cardiff City Stadium has shifted dramatically following the misery of Championship relegation last season.
But Barry-Murphy, who joined the Bluebirds as head coach in June, wants more from his team as they head to Wigan Athletic on Saturday:
BBM:
"We played really well [at Burnley] on Tuesday and got what we thought was a deserved victory, but we can still do a lot better in certain elements of our game," he said.
"We have an awareness that we are still in the early stages of the season. There's a tiny minority of games gone and we have a lot of improving to do.
"We are confident that if we can reach the levels of intensity we did for large periods of Tuesday more often, and with better quality, then we will be fine."
Cardiff have slipped to fourth in League One after home defeat to Bradford City last weekend.
The Bantams are now three points better off than Cardiff at the top of the table – although Barry-Murphy's side have a game in hand.
"I think you saw when we played Bradford, we didn't play without the ball how we wanted to," Barry-Murphy added.
"Our pressing was not consistent enough and we didn't defend against them in any way, shape or form the way we'd want to.
"In possession we were okay, we created good chances but weren't good enough to take them. But you saw what it looked like on Tuesday what when we played with the intensity we want."
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