Rochdale fans stayed to applaud their team off the pitch at the final whistle after the third-tier club earned a second FA Cup replay.
In 2018, they forced a 2-2 draw against Tottenham Hotspur before losing the return at Wembley.
"It's a huge result for the club," added manager Barry-Murphy. "I was a little disappointed with the way we played in the first half but the way we finished was important. It felt like a second-half to be proud about."
On earning a replay at St James' Park, he added: "We don't complain about the fixture congestion. We relish it in the cup. It's what the club's about and we're delighted for that to continue."
Both clubs go into the draw tonight, and on this showing, this tie is far from being a formality.
United fell apart second half as Rochdale players looked the more fitter.