Substitute Joel N’Dala fired home in stoppage time to preserve our unbeaten start to life in Group G.
The visitors, who had also won each of their opening two matches of the European campaign, had taken the lead early in the second half through a Noah Sahsah solo effort.
But City’s persistence would eventually pay off, ensuring we remain top of the pile at the midway point in the round.
And Barry-Murphy was pleased to see his side finish with a flourish at the Academy Stadium.
“I felt as if we always could get a positive result. I thought we played well in patches,” he reflected.
“Obviously there were parts where we could have been better, but to see the lads going until the end, keep trying to score a goal and create chances in the way we play, I was very proud of the way they finished the game.
“The nature of this competition is how testing it can be and the different qualities we will face.
“To provide enough chances late in the game to score and possibly go on and win the game was satisfying for me knowing we can do a lot better.”
Hear the boss’ thoughts in full via the video above...