Villa beat the division’s bottom side through an own goal from Will Vaulks and Jonathan Kodjia’s late second to register a first away win of 2017.
But the game was littered by missed chances, and until Kodjia made the game safe a spirited Rotherham threatened to make Villa pay for their wastefulness.
In the end they got the job done for a third win in a week, which has eased any niggling fears of being pulled into a relegation fight.
“It was an awful six weeks, I can’t deny that,” Bruce said.
“But when I look back at the Ipswich and Nottingham Forest games, we did enough to win those games.
“We had 50 shots on goal and I thought it was going to be something similar today.
“We have missed so many opportunities, we could have been three up in the first half. In the end it took an own goal to make the breakthrough.
“I was always confident we could get one because of the law of averages, but there was a nagging worry that it might be another one of those afternoons.
“We have done enough to win the game.”
For Rotherham it was a 26th league defeat of the season, and now 18 points adrift of safety their relegation is only a matter of time in coming.
They could have been three or four down in the first half as Lewis Price twice saved well from Albert Adomah and Conor Hourihane, while Aimen Belaid produced a heroic goalline clearance.
Villa had some luck in their opening goal as Vaulks could only turn Adomah’s cross into his own net. And after Bruce’s men weathered a Rotherham onslaught, Kodjia put the game in the bag with a low finish.
“Hand on heart they were better than us and deserved the win,” interim boss Paul Warne said.
“My job and 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.
“I am proud of the way they played at the end but I am disappointed with another defeat. We are doing everything to stop the rot so as long as people can appreciate it.”