The South Yorkshire rivals were both relegated from the Championship last term, with the Millers emerging victorious in both league meetings last season.
This time around it was the Owls who took the bragging rights as second-half goals from Florian Kamberi and Lee Gregory saw the visitors take the spoils.
Bailey Peacock-Farrell was the hero for the away side as the Northern Ireland international pulled off a stunning save to keep out Kieran Sadlier’s penalty after Callum Paterson had brought down Joshua Kayode.
“Apart from the last 20 minutes, I was really pleased," reflected Warne.
“We were the better team first half. The penalty miss before half time was a big thing.
“His (Peacock-Farrell’s) was a really impressive performance and he deserved his clean sheet. You go in at half-time all square and it gives them a lift.
“I believed we were going to score an equaliser. When the second goal goes in, which was a rare mistake, the lads just looked a little bit beaten, truth be told.
“I think they felt a little bit sorry for themselves and I don’t know if they had a real belief that they would get back into it. But up to then I thought we were really good.
“It was a good performance but ultimately it’s the scoreline that matters.”