The Bluebirds are now four points behind leaders Lincoln following a 1-1 draw at Barnsley and have had their own lead over Bolton cut to nine points.
For all three top clubs, there are 10 matches to go and 30 points still to play for.
Rubin Colwill’s early strike had given the Bluebirds the lead at Oakwell, but Scott Banks’ equaliser ensured the points were shared and prevented Cardiff from closing the gap at the top.
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Despite the setback, Barry-Murphy stressed that difficult results and setbacks are simply part of the challenge of a long league campaign.
“I’m looking at our own team to make sure we’re improving all the time,” he said.
“The league campaign is never meant to be straightforward or easy. If it was everybody could do it and it wouldn’t be as rewarding when you achieve something.
“The ambition of the dressing room is clear for me to see. I can feel it every single day.”
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Cardiff began brightly and almost fashioned the first opportunity when Omari Kellyman pressed Barnsley goalkeeper Owen Goodman.
His challenge turned into a shot that rolled just wide of the post.
The visitors soon made their pressure count. In the 11th minute Jack Shepherd’s mistake allowed Ollie Tanner to swing a cross into the area, where Colwill was waiting to finish confidently past Goodman.
The Bluebirds had a golden chance to extend their advantage moments later when Calum Scanlon found Tanner unmarked at the far post. However, the winger could only scuff his effort wide, allowing Barnsley to escape.
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That miss proved costly as the hosts levelled before the break. Tom Bradshaw delivered a cross into the box which Banks controlled before calmly finishing to bring Barnsley back into the contest.
Barnsley nearly went into half-time ahead when David McGoldrick was presented with a clear opportunity from close range, but the experienced striker fired well over the bar from 10 yards.
Cardiff continued to search for a winner after the interval. Cian Ashford threatened and Colwill also tested Goodman, yet the Barnsley goalkeeper stood firm to deny the visitors a second goal.
Barry-Murphy acknowledged that his side had created the opportunities to take control of the match but were ultimately punished for failing to convert them.
“It was a difficult game,” he said.
“We attacked from the first minute. We scored a great goal and then Ollie Tanner’s chance was a great chance for us to extend our lead and dominate the game completely.
“But we didn’t, and Barnsley scored a goal from a breakaway.”
The draw leaves Cardiff still firmly involved in the race at the top of League One, though they now trail Lincoln by four points.
Barnsley, meanwhile, remain 12th in the table, seven points adrift of the play-off places but with two games in hand that could strengthen their hopes of climbing into contention.
Reds head coach Conor Hourihane was pleased with the way his team responded after recent work on improving their performances.
“I think the biggest thing is from the Wycombe game, we did a lot of work on how we wanted to get better and improve,” he said.
“They put a winning performance on against Exeter.
“They come here not fancied, and they’re putting in a performance like that.”
Hourihane also pointed to the demanding schedule his side must navigate in the coming days.
“It’s going to be a challenge – the schedule’s busy and we don’t have the biggest squad,” he said.
“We’ve got three games next week so can we have one big effort and pick up as many points as we can?”
