The Leeds midfielder scored a late equaliser against Gary Rowett's men.
Leeds drew 1-1 with Birmingham after going down to an early penalty. But Murphy hit back with a late equaliser and Redfearn feels the midfielder produced a brave performance, while also admitting he has had it tough at Elland Road recently.
As ever, the 49-year-old also praised wonderkid Lewis Cook for his contribution against Birmingham.
Redfearn praises the "brave" Murphy, who has "had it tough". Also thinks Cook "had a great game" - "He can play anywhere in midfield." #lufc— Leeds United FC (@LUFC) January 17, 2015
Meanwhile, the Leeds boss believes it would have been a travesty had the Yorkshire side not earned a point against Gary Rowett's Birmingham side.
A key theme is developing, however, in that Leeds are not taking their chances - and not winning games.
Week after week, Redfearn praises his side for their effort without the three points to show for it, although it is certainly an encouraging sign that Leeds' performance levels have risen of late.
Courtesy of goal difference, the Elland Road outfit have risen a place in the Championship table after their draw with Birmingham.
Redfearn says "it would have been a travesty" if #lufc hadn't taken a point: "We were camped in their half in the second half."— Leeds United FC (@LUFC) January 17, 2015