While they defeated their League Two opponents comfortably in the end thanks to Callum Wilson and a double from Carl Baker they were second best for large periods with Murphy superb throughout.
The shotstopper saved from Michael Smith, Harry Pell and George Porter during the first half and manager Steven Pressley claimed his contribution was vital.
"Joe Murphy was outstanding," he said.
"In the first half we would have found ourselves several goals down if it hadn't been for Joe Murphy.
"He's been having a very good season for ourselves, he's a big influence on the group and I'm delighted with him.
"My pre-match briefing was 'no excuses tonight'. We know our system, we know exactly our roles and responsibilities within that, we know how we can play and if we do that we win the game.
"Although it took us a little bit of time when we finally applied our principles, in the end I thought we were excellent.
"It was a very difficult game. In the first half it's probably as poor as we've played in a number of weeks or months.
"But I thought the response of the team in the second half was terrific, especially going behind in an FA cup tie away from home in what is potentially a banana skin tie, so all in all I'm delighted."