The Irishman guided Cardiff to five wins and a draw in their opening six matches, leaving the Bluebirds unbeaten and top of the table with 16 points, level with Doncaster but with a game in hand.
They also rounded off the month with a commanding 4-0 victory over Plymouth Argyle.
Yet, despite those plaudits, Barry-Murphy is demanding more.
The 47-year-old, who was appointed in June following Cardiff’s relegation from the Championship, believes his side cannot continue to rely on moments of individual brilliance to win tight games.
"I thought we played well in both games,” he said of Cardiff’s recent away victories at Wimbledon and Luton.
“But on another day at Wimbledon we could've conceded and lost the game and it was the same at Luton. (Goalkeeper) Nathan Trott made several spectacular saves.
"But also, we did play really well in both games. I suppose we're looking to improve as the season progresses with our performances to give us the very best chance to win.
"We're really clear there is a lot more work to do. For us, since the game against Plymouth, we had a chance to look at all of the games really closely and look at what went well and what you can do better, and there are a lot of things we can improve.”
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That focus, he stressed, is particularly on Cardiff’s forward play.
"A lot of the matches have been in the balance. You look at the game against Port Vale and we could have lost. The game against Wimbledon was in the balance; a 50/50 game. And Luton was very similar.
"But we have been reliant on some spectacular goals to put us on our way. We need to improve a lot of our attacking play to give us more of the movements that we can rely on.
"We can't always rely on Ryan Wintle scoring from 40-yards. That's a great finish and one that we're very happy to celebrate but you score them around three times out of 100.
“You can't over rely on those moving forward. We have to get much better at our attacking actions to give ourselves substance to the way we want to play."
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Barry-Murphy’s candour comes during a week when Cardiff also celebrated individual recognition.
Dylan Lawlor, the 19-year-old centre-back, was named EFL Young Player of the Month after starting every league match in August and marking his rise with a man-of-the-match international debut in Wales’ 1-0 win over Kazakhstan.
Lawlor’s performances, combined with Cardiff’s resilience at the back, have helped them keep four consecutive clean sheets.
But the defender has also echoed his manager’s confidence in what the team can achieve this year.
“You’ve always got to have the belief that you can make a start like we have,” said Lawlor. “We’ve got the belief that we can get promoted and absolutely batter the league.
“Our goal is to get the club back into the Championship and then get back into the Premier League. Promotion isn’t a banned word, it’s what we want.
“The mindset Brian has brought in is ‘why can’t we just go and annihilate the league and get promoted’. We’ve got the quality.”
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Cardiff head to Stockport County this weekend, aiming to extend their unbeaten run against a side who sit ninth but were contenders at the top end of the table last season.
While optimism is high, Barry-Murphy remains adamant that progression depends on sharpening their offensive play.
The manager, who previously coached at Rochdale, Leicester City and within Manchester City’s academy, had made defensive solidity a foundation but knows goals will ultimately also dictate Cardiff’s promotion prospects.
