Ollie Watkins just after halftime as Villa grabbed the points on Saturday.
“In many ways, it was an even game," said Frank. "The first half was very even, neither team could really break the deadlock and there were not many decisive moments.
“In the second half, they scored the goal with the deflection which helps. Other than that, we were completely on top in the game.
“We tried crosses into the box and created a lot of dangerous situations, but didn’t have the killing touch on the night. It was a game where I think we deserved much more than what we got."
Bees defender Ethan Pinnock also reflected: "It was a tight game. The first half was fairly even and we were well within the game.
"We conceded early in the second half but, after that, we stepped up, created some good chances, got ourselves into some good positions, but it didn't fall for us today."
He added: "Overall, we defended well. They've got a lot of good attacking players, one-v-one players, creative players and, for most of it, we contained it.
"Looking at the other side of it, it was just about trying to nick a goal, which we didn't manage to do today."