The Millers led 1-0 through Richard Wood's goal but conceded just before the half-hour mark before two goals either side of the break propelled Hull into a 3-1 lead.
Despite Jamie Proctor's late strike, the hosts couldn't prevent a first home defeat of the season.
"The game was defined, unfortunately, by one minute either side of half-time," admitted Rotherham boss Warne.
"We took a decent lead and every time we made ventures into the box we looked a threat.
"I was disappointed with their first goal and the second was right on half-time which is pretty inexcusable.
"And then the third goal was an individual error again.
"They need to learn quick but we've learnt something from each game we've played.
"There were some errors but as long we learn from the errors and try to eradicate them for the rest of the season, then I'll be happy."
The Millers will look to get back to winning ways on Sunday when Millwall visit the New York Stadium.