But Villa manager Steve Bruce was full of praise for Scott Hogan after the forward netted twice.
Hogan had an unhappy start to life at Villa Park following his move from Brentford last January. He dropped down the pecking order to fourth-choice striker, but is now the club’s danger man after scoring four goals in three games.
The 25-year-old demonstrated he has found his best form in recent weeks by sealing Barnsley’s fate with his two goals in the opening seven minutes.
Conor Hourihane scored Villa’s third shortly after Dimitri Cavare had pulled a goal back for Barnsley, who remain just above the relegation zone.
“The writing was on the wall when we went two goals behind in the first half,” said Heckingbottom. “Besides giving Villa too much respect, the goals we conceded were shocking and we were up against it from the start.
“We had four defenders back and Hogan got between two of them to score the opening goal and he was the smallest man in the box when he scored the second. We had a chance for their third and if we make such mistakes we are going to be beaten.
“I know we missed chances in the second half, but it is easy to play when you are 3-1 down. I want that no-fear mentality from the start of a game.”
Aston Villa: Johnstone, Elmohamady, Chester, Terry, Hutton, Bjarnason, Snodgrass, Grealish, Hourihane (Whelan 86), Adomah (Onomah 77), Hogan (Davis 90). Unused substitutes: Neil Taylor, Lansbury, Elphick, Bunn.
Barnsley: Davies, Cavare, McCarthy (Hammill 46), Lindsay, Pinnock, Yiadom, Potts (Mottley-Henry 68), Mallan, Moncur, Moore (Thiam 73), Bradshaw. Unused substitutes: Townsend, Pearson, Brown, Wolfe.
Referee: S Duncan (Tyne & Wear).