Dylan Stephenson's composed finish opened the scoring in the closing stages of the first-half at Heritage Park, the Blyth-born striker's fourth goal in his previous Premier League 2 matches.
After keeping Boro at bay for the majority of the second-half, with Matthew Hoppe striking the crossbar for the hosts, Joe Gibson's stoppage-time strike denied Newcastle a first away win of the 2022/23 season, leaving Murphy and his team-mates frustrated at the full-time whistle.
The 18-year-old centre-back, who has represented Republic of Ireland at under-19 level, told nufc.co.uk: "It felt like a loss. We defended so well in the second-half as we were literally camped in our own half and were making block after block.
"To concede in the last few minutes is very disappointing and we also had a great chance to win it at the end. It's difficult to take but it's a tough place to come and they are near the top of the table so it's a decent point.
"We are ten seconds away from a happy changing room but instead we're feeling a bit down and sad. That's football - it happens sometimes and we just need to move on from it and make sure we take a clean sheet from our next game."
Newcastle's youngsters, who currently occupy sixth place in Division Two, will head back on the road in a fortnight's time when they travel to the West Midlands to face their Aston Villa counterparts at Bodymoor Heath Training Ground.
Murphy believes the squad can learn from their difficult blow against Boro while the Irish teenager reflected on a number of encouraging spells for United's under-21 side.
"We can still take positives from the game," the Galway-born defender added. "We played very well in the first-half and got on the ball a lot and we created chances.
"In the second-half, I think we just sat in and were looking to see out the game. It's a tough place to visit like I've said but we will learn from it and turn our attention to the next match.
"We're still moving in the right direction. We didn't lose and played well in parts. We have two weeks now to prepare for the next game (against Aston Villa). Next we are one-nil up, we'll try and make sure that it doesn't happen again."
