James McAtee opened the scoring early in the second half before two quickfire goals from Blackburn's Ashley Phillips and Daniel Pike saw the visitors take the lead at the Academy Stadium.
But just three minutes from time, McAtee looked to have saved City a point with a finely taken free-kick before going one better with a 90th minute strike to see City retake the lead and complete his hattrick.
Romeo Lavia added a fourth deep into injury time when he nodded home his saved penalty and Barry-Murphy was delighted to see how his players responded to going behind.
He reflected: "In these situations when things go against you, you learn so much in terms of our resilience and our mentality.
"To see that way the lads battled back and kept trying to play against a team who were very good on the night was a testament to the players’ ability and courage.
"When things do get difficult, things go against you and you feel hard done by it is easy to find excuses but the mentality of the group means I feel like I can push them very hard."
And whilst McAtee's hattrick stole the show on the pitch, Barry-Murphy explained how his number 10's leadership off it is benefitting the young blues.
"It was very hard for James to operate in that space but the discipline he showed to hold his position and work for his teammates carries on from Sunday," he highlighted.
"You are seeing him being one of the more senior players in this group and looking after Micah (Hamilton) and Shea (Charles) who are making a first appearance of the season and Oscar (Bobb) so to see him develop that leadership is a very important part of his development.
"It is great when everything is going your way but I think the real beauty is in the difficult moments when you feel as if you have been hard done by or something hasn’t quite gone your way and how you react and stick to the plan."