The Millers went down to two first-half goals from Rudy Gestede and a late effort from Jack Grealish in front of a crowd of more than 33,000, including 2,000-plus away fans, at Villa Park.
"I thought the players stuck at it. It's a long season. We're not going to get too downhearted," said Stubbs after taking charge of his third competitive Rotherham fixture.
Rotherham were matching their opponents, who were in the Premier League last season, until a mix-up between Jon Taylor and Jake Forster-Caskey in the opposition half led to the home side breaking away and scoring in the 21st minute.
"We're always disappointed to lose," Stubbs said. "I thought up until the first goal we were in the game. We needed to show a little bit more belief when we had the ball.
"The first goal was disappointing. It came from an unforced error. The second one, we could do better too. You have to be realistic as well when you look at resources."