Oliver Norwood’s penalty had appeared to condemn the Bluebirds to their first defeat of the campaign, but they struck late to salvage a 1-1 draw at Stockport County.
Yousef Salech rose seven minutes into stoppage time to head in Chris Willock’s cross and rescue a point.
For Barry-Murphy, the manner of the response said everything about his squad’s resolve.
“We hadn’t had any real adversity or anything go against us before today because we have been so good,” said the Cardiff boss.
“We're playing against a team who are very strong at home. We didn't find our rhythm early on.
“For us to show the character that we did in the second half and bounce back from what wasn't, to our standards, a great first half is testament to the players.
“The commitment and ability to keep going until the end was what pleased us most.”
Barry-Murphy admitted that his side’s sluggish start merited the half-time deficit, but he was equally encouraged by the shift in intensity after the break.
“Our first-half play was not what I wanted it to be and as such we deserved to be behind at the break,” he said.
“At half-time, I was looking for a reaction from the players and for them to understand what it felt like to increase performance levels and it was so pleasing to see this.
“It was a great cross from Chris to service the goal. I thought we looked quite dangerous at the end of the game.
“We tried to be as aggressive as possible, to get a lot of attacking players on the pitch and go forward. Fortunately, we scored that goal.”
For Barry-Murphy, bravery was as important as quality in ensuring Cardiff found a way to avoid defeat.
“I think all of our strikers – Yousef, Callum Robinson, Isaak Davies, as much as I say it is about the team, and we score goals as a team, they want to score because it fuels them,” he explained.
“It was a great cross from Chris [Willock] to service that. We tried to be as aggressive as possible. We put all of our attacking players on the pitch and went for it.
“Sometimes fortune favours the brave.”
READ MORE: Brian Barry-Murphy Insists Cardiff City Must Sharpen Attacking Edge Despite Flying Start
While the Cardiff manager praised his players’ refusal to yield, Stockport counterpart Dave Challinor could not hide his frustration at how his side let victory slip away.
“I am pleased with the first-half performance. We need to get into a situation where we can perform like that for longer,” said Challinor.
“Probably up until 60 minutes we were really aggressive in terms of our press and probably lost a little bit of impetus after that.
“But to concede in the manner we did is obviously disappointing and leaves a sour taste on what should have been a really positive afternoon for us.
“Naturally, you have to put the goal we conceded partly down to concentration and there are some tactical and technical bits we need to do better.
“You can’t be conceding a goal from a free header in the middle of your goal on the six-yard line.
“We can’t concede a goal like that, it doesn’t happen to a team that is going to be at the top of the league. Ultimately, that’s where our aspirations lie.”
READ MORE: Dylan Lawlor Insists: I’d Be Stupid to 'Turn My Head' From Cardiff City
Stockport had looked in control for long periods, with Benony Andresson hitting the post before winning the penalty that Norwood converted.
Andresson continued to trouble Cardiff throughout his 73 minutes, and Nathan Trott had to produce a superb save to keep his header out.
But Cardiff refused to fold, and in stoppage time Salech – who had already seen one goal ruled out for offside – finally found the target with a deft header.
READ MORE: How Cardiff City "Won" the International Break Under Brian Barry-Murphy
