The Millers conceded twice from two finishes of real quality, from Conor Hourihane and Matt Grimes respectively, in the first half.
That forced Warne into some tactical tweaks at the interval, with Freddie Ladapo also introduced as Rotherham aimed to extend their three-game unbeaten run.
Ladapo pulled a goal back with a well-placed header but Jay Fulton restored the visitors' two-goal cushion with an instinctive finish to complete a devastating counter-attack.
"They are an excellent team. I have full respect for Swansea and the way they play," reflected Warne.
"They have got good players and they have strengthened again, you can just see Hourihane's quality, he is like the best kid at school.
"His first goal is a great finish. When we went in at half time we had to tweak the way we were playing but I didn't think there was much in it really.
"The second goal was avoidable but it was still two really good finishes."
The Millers chief felt the support of the Rotherham fans might have pushed his side to another level as they now look to a crucial meeting with Derby County on Tuesday night.
He added: "I just thought that we if ever we needed a crowd in, it was today. We didn't quite have that energy or drop on that many second balls.
"It wasn't like our goalkeeper made four great saves to keep us in it, they were just really good finishes.
"We didn't have enough injection of pace to win second balls for my liking.
"We changed it second half, I thought Ryan Giles came in and did really well. We put Freddie up, man marked them in the middle a little bit more and had a bit more impetuous really."
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