The Millers were beaten 2-0 at Elland Road as goals from Mustapha Carayol and Souleymane Doukara gave Steve Evans victory against the side he managed for three years and booked Leeds' place in the fourth round.
But that does not tell the whole story as Redfearn's side matched - and even outplayed - Leeds for large swathes of the game but carried no goalscoring threat.
They were then undone by a wonder strike from Carayol and an embarrassing defensive mix-up between Lee Camp and Frazer Richardson, which allowed Doukara to walk in the second goal at the death.
Redfearn was entirely content with the performance, but bemoaned a lack of cutting edge.
"We were just missing a bit of quality, but that quality costs a lot of money," Redfearn said.
"Good players don't come for nothing. As a performance I have got to be pleased with the application, the way we worked.
"I thought we closed down, we pinched play we got our tactics right again, Leeds looked predictable in the first half and that was down to us.
"But the first goal was a superb strike and there's nothing you can do about it and then the second goal is a cock up.
"You can’t legislate for things like that, especially when you are 1-0 down and chasing the game when we were the better of the two sides at the time.
I"t's a lack of concentration and it goes into the fact that when we're on top and we were, don't let anyone tell you any different, we have got to score.
"We have to try and get our noses in front. If we go 1-0 up it would have been a different Elland Road and we know that. But you're open to the break or them having a little spell.
"They had a little 10 minutes and they scored.
"But as a performance it was decent, we have come to Leeds twice now and there has been nothing between the two teams.
"They are a big club, for us to compete and match them is good for us. It's disappointing with the result, but we have got to move on and get ready for a big game against Brighton on Tuersday."
Neither Camp or Richardson came out of their mix-up with much credit, but Redfearn says the goalkeeper should have cleared everything in his sights.
"The ball was rolling back to goal and the keeper was running on to it so it has got to be the goalkeeper.
"For me he has got to clear the lot, ball, defender, striker, the whole lot.
"Listen, Lee Camp has been fantastic for us, particularly recently, he has been one of our stand out players but those little mistakes are disappointing because it undoes some good work.
"2-0 flatters Leeds today, they probably deserved to go through, but I thought we matched them."
