The loss at Villa Park was Arsenal's third game in seven days, and it brought them crashing back down to earth after beating Premier League champions Liverpool and Pep Guardiola's Manchester City to reach the FA Cup final.
Arteta revealed his disappointment following the loss, but admitted the past week has been demanding on his squad.
"I am really disappointed with the result," he said.
"I cannot fault the effort of the players, for sure. The boys are really disappointed. They wanted to keep building momentum.
"It's been a really demanding week emotionally and physically for them, and I know how much they wanted to win today again to give us a chance to qualify for Europe from the Premier League. But we're going to try in the final."
The Gunners failed to register a shot on target against Dean Smith's relegation-threatened side, with Arteta admitting his team lacked a 'spark' in attack.
"You could see how they were going every time we lost the ball, how aggressive we were, Villa couldn't put three or four passes together.
"We completely dominated, we played in the opponents' half but we missed that spark and the ball in the final third to create more.
"We knew about Villa's set-pieces, we conceded another goal there and it cost us the points."