The London club were beaten by the Birmingham-based team away from home.
Villa scored thrice early in the game, while the Bees did get one back later on.
“We didn’t hit our highest level today," said manager Thomas Frank.
“We faced a very good Aston Villa team; you could see the difference between the two teams today, as to why they’re playing Champions League football and we’re not, unfortunately.
“I know we are better than what we showed today, that’s the frustrating part. But we faced a team who hit a high level.
“They got the first goal - a top action from (Morgan) Rogers, what a player, by the way - and then, of course, the penalty, which I’m really doubting is a penalty. But we didn’t lose because of that, they were just better than us over 90 minutes.
“We didn’t stop the transitions well enough and we lost the ball in certain situations.
“The positive was that we were better in the second half, but we weren’t really close to getting anything out of the game.”
“It was a tough first half," added Danish midfielder Martin Damsgaard.
"We played okay on the ball but they killed us on the counters. We need to be quicker to react, sprint back and stop the counters - maybe we have to make a foul sometimes.
“A lot of players were talking at half-time saying we needed to be better and that, even though it was going to be a hard second half, we had to express ourselves and I think we did that. I think we were better in the second half but it’s difficult to come back from 3-0 down.
“I hoped that my goal could start something but it didn’t. We tried to play offensive in the second half but we made it hard for ourselves with the first half."
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