The visitors scored the only goal of the game through John Sands after half an hour, with Rovers denied what looked like a clear penalty when Keshi Anderson’s shot was handled on the goal-line.
Byrne said: “We have to move on very quickly and take pride out of what we have achieved on this FA Cup run.
“It was a very tough physical game which at times exploded with some heated exchanges between players as expected in such a high profile FA Cup clash.
“We came off the pitch very disappointing at losing the game but felt that we had done enough to earn a replay at least with us by far creating more opportunities on goal,
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“It was nice to see Ben Sawyer playing more like I know he can, running at players and causing problems and as always Tony Burnett was a great up front.”
To read more from Byrne, plus a full report, see the News Gazette on sale now.