Boss Paul Warne made no excuses after an eighth Rotherham United defeat in nine matches saw the gap between his side and Championship safety grow to 18 points.
The Millers turned in a spirited performance but were beaten by two second-half goals by Aston Villa at New York Stadium.
“Hand on heart, they were better than us and deserved the win,” the caretaker manager said.
“My job, and my remit off the chairman, is to win as many games as I can and send the fans home happy. The lads gave me everything, but it wasn’t enough to get the goals to win the game.
“I don’t claim to be a super manager. The lads are giving me everything they have got, but we haven’t possibly got that little bit of class.”
Bottom club Rotherham, who are at home to Brighton on Tuesday, were hit by more injuries, with Stephen Kelly, Danny Ward and Jon Taylor all forced off the field.
They fell behind when Will Vaulks, moved from midfield to stand in for Kelly at right-back, put Jonathan Kodjia’s cross into his own goal after 68 minutes.
Kodjia fired home the second with three minutes remaining, ironically after the Millers’ best attacking spell of the game.
“I am proud of the way they played at the end, but I am disappointed with another defeat,” Warne added. “We are doing everything to stop the rot.”