Leeds had won seven of their last 10 league games heading into the Forest fixture and were playing in front of their biggest crowd of the season.
Visitors Nottingham Forest, however, restricted Leeds in front of goal and kept a clean sheet.
Redfearn was happy enough with the point and also praised Leeds' own defending.
But the 49-year-old was aggrieved 21-year-old Taylor could not convert what he thought was the best chance of the game.
Asked if it was a fair result, Redfearn said: "Probably, I think we had the best chance - the one that fell to Charlie Taylor. Listen, Eddie [interviewer Eddie Gray] he's got to score, mate! It's a great chance.
"Other than that, it was just two teams who had been doing well who locked horns and the pleasing thing, from our point of view, is that I thought we played well enough and I thought we defended well. We looked solid enough at the back."
A point does little for Nottingham Forest's slim play-off hopes but is nevertheless an achievement considering some of the Championship sides Leeds have beaten at Elland Road in recent weeks.
For Leeds, a point ensures their recent run hasn't come to an end but their inability to score prevented them from achieving their eighth win in 11.
The Yorkshire side travel to Fulham next, where they will come up against two ex-Leeds strikers in Ross McCormack and Matt Smith. Forest, meanwhile, host Rotherham United during their next Championship action.