The Bluebirds won the North v South Battle of Cymru to secure their place among the last eight.
“I’d love to be back at our own stadium,” said Barry-Murphy after overcoming Wrexham in the all-Welsh clash in north Wales.
“You’ve seen the distance our supporters have had to travel in midweek to Burnley and here tonight.
“For them it would be great if we get back to our home stadium, which would be a great occasion for us all.”
The win — Cardiff’s first appearance in the Carabao Cup quarter-finals since their 2011–12 final run — capped off a night of pride and composure for Barry-Murphy’s team, who outplayed their hosts in the first meeting between the two clubs since 2004.
“It was a tough game for us but we played in the way that we wanted to play from minute one, and I suppose showed our character and our skill level throughout the course of the game,” he said.
“So, it was very satisfying and I am immensely proud of the whole club.”
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Cardiff’s intent was clear from the opening whistle.
They dominated possession, created 23 chances, and dictated the tempo throughout, with Yousef Salech firing them into an early lead before Will Fish sealed the win late on.
Wrexham’s Kieffer Moore equalised against his former club with a towering header midway through the second half, sparking hopes of a home comeback.
But while the Hollywood-owned League Two side fought hard, this was a night when Cardiff’s discipline and control shone through.
Barry-Murphy, who is enjoying his first major cup run since taking charge, said the result reflected both the mentality and commitment he has been trying to build within the squad.
“It’s a new experience for me and I think it’s very exciting for the players,” he explained.
“I think you have a choice at the start of this competition how seriously you want to take it, and when you do take it as seriously as we have done you’re always hopeful of progressing as far as you can.”
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That seriousness has paid off. Cardiff have beaten higher-division opponents and battled through long away trips to reach the last eight, a feat that clearly means something to their Irish head coach.
“The uncertain nature of who you’re going to face in the next round is what makes it so exciting,” he said.
“But for us, I’d love it if the next one was at home. It would mean so much for the players and supporters.”
Barry-Murphy’s measured enthusiasm stood in contrast to the mood in the opposite dugout.
Wrexham boss Phil Parkinson admitted his team fell well short of the standards they have set in recent seasons, particularly during a first half in which they were comprehensively second best.
“We were off the pace first half,” Parkinson said.
“That's probably an understatement. We didn't close down with enough aggression or intent, and made it too easy for them.”
“Then in the second half I thought the changes got us back in the game, and I felt we could go on and win the game but we probably didn't produce the right decisions at the right time in that top third of the pitch.
“We're hugely disappointed. We knew it was an important night for us, the supporters.”
Wrexham were booed off at the break, and while Moore’s equaliser gave them brief momentum, their defensive lapses returned almost immediately as Fish restored Cardiff’s advantage.
Parkinson, who made several changes to his starting XI, accepted responsibility for the result.
“We've had lots of praise over the years and we'll take the criticism, myself included, for going out the cup tonight,” he said.
“We made a lot of changes and I'm sure everybody will be analysing that, like myself, but I did it for the reasons I thought were the right ones with the schedule we've got coming up.”
For Cardiff, though, the night belonged to their growing belief under Barry-Murphy.
The head coach has repeatedly spoken about embedding a distinct style and mentality into the squad, and Tuesday’s composed performance against a spirited rival showed that philosophy taking root.
“It was a tough game for us but we played in the way that we wanted to play from minute one,” he reiterated.
“We showed our character and our skill level throughout the course of the game.”
Now, all eyes turn to Wednesday’s quarter-final draw, which takes place after Newcastle’s tie against Tottenham.
Cardiff, who have already defied expectations to reach this stage, will discover who stands between them and a potential semi-final spot — and Barry-Murphy is clear about what he wants next.
“For them [the fans] it would be great if we get back to our home stadium,” he said again. “It would be a great occasion for us all.”
