The Millers went down to a fifth loss from seven games against the Bees, who scored second-half goals through Marcus Forss and Ivan Toney.
Warne's men were unable to reproduce the levels that saw them draw 2-2 with Bournemouth at the weekend and the boss conceded his side were beaten by better opposition.
“I go home as proud as I did on Saturday, we got beaten by a better team, boo hoo,” Warne said.
“I thought they controlled the second half and we edged it first half. It was a close game in my opinion.
“The first goal was always going to be crucial and unfortunately it didn't go to us.
“I thought we were really good first half, as good as we could be really.
“We limited them to very few chances, we worked really hard off the ball, we were a bit rash on it at times and we created a few half chances that if you are going to beat the top teams you have to take really.”
Brentford's second goal came from the spot, after a foul which Mickel Miller picked up a second yellow card.
It was the sixth penalty the Millers have conceded this season, the most in the division.
“There was enough contact for a penalty,” Warne added.
“You talk about the smallest of margins, Matt Olosunde weaved through the penalty box in the first half and I think if he goes to ground it would definitely have been a penalty.
“If you're honest and stay on your feet you don't get rewarded.
“ I have got no complaints with the penalty and no complaints with the result because they created better goalscoring opportunities than we did.
“But I haven't got any complaints with the lads' effort.”
Warne felt his side were feeling jaded after the exertions against the Cherries.
“Definite fatigue. The three central midfielders gave everything, as they did on Saturday,” the boss added.
“The goal knocks the stuffing out of us and we did look jaded in the second part of the second half but I was expecting that so I was hoping we would have been five up by half-time so it would have been easier in the second half.”
The Millers face a crunch game with fellow strugglers Coventry City on Saturday.
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