Villa struggled to respond to falling behind to Jefferson Lerma's second-minute goal at the Vitality Stadium and rarely threatened an equaliser before Kieffer Moore's late header sealed victory for the Cherries.
Gerrard, who has designs of a top-10 finish this campaign, cut a frustrated figure for most of the afternoon and was left to lament his side's lack of cutting edge and inability to deal with balls into the box.
"We have ourselves to blame and it's important that we don't just focus on the two set-play goals we conceded because across the board, across the 90 minutes we haven't had enough quality in the final third," said the Villa manager.
"It's extremely disappointing, certainly not the result we came here for but I don't think we can have any complaints in terms of the outcome of the game.
"The good thing is, it's glaringly obvious where we went wrong. Watching the game (again), I don't think I will be surprised by anything."
Danny Ings, preferred to Ollie Watkins from the start, and Jacob Ramsey tested Mark Travers following Lerma's opener.
Villa debutant Boubacar Kamara was later narrowly off target from distance, prior to Moore sealing victory for the hosts, while playmaker Philippe Coutinho was a peripheral figure for most of the afternoon.
"We've had enough quality players on the pitch but our last pass, our last cross, our last inventive spark was off today for sure," continued Gerrard.
"We put all our attacking quality on the pitch but we couldn't find the answers in the final third. That's on me, that's on us."