Arteta's side would have gone back to the top of the table with a victory at the Emirates Stadium.
But instead Arsenal were beaten for the first time in 12 league games as two goals in the last six minutes from Leon Bailey and Ollie Watkins rocked their title dreams.
The second-placed Gunners are two points behind leaders Manchester City with six games left in their bid to be crowned English champions for the first time since 2004.
Facing the prospect of blowing the lead in the title race for a second successive campaign, Arteta issued a plea for his team to stick together.
"That is the reality right now. We knew this moment could come. Now it is about reacting in the right way and keep believing," he said.
"Now is the moment to stand up as leaders and show character. We don't have any other solution. When you win and win and win, it is easy. Now is a big test for us.
"If you want to win the Premier League and Champions League, you have to stand up."
City will lift an unprecedented fourth successive Premier League title if they win their remaining games.
It is a stark reality for Arteta, whose side had won 10 of their previous 11 league matches.
"We cannot control that. In any other league in the world if you won the number of games in a row that we did, you would be six or eight points clear. That is not the case here. That is the challenge," Arteta said.
"We had one of the best performances we had all season in the first half. It should have been three or four. We couldn't do it in the second half, the momentum shifted.
"It is now about how we react after this blow. This is in our control."
'Frustrated and sad'
Held to a 2-2 draw by Bayern Munich in the Champions League quarter-final first leg on Tuesday, Arsenal now head to Germany for the second leg on Wednesday looking to stop their season falling apart.
"The players are frustrated and sad but we have a beautiful opportunity to go to the Champions League semi-finals for the first time in 15 years. It cannot come at a better moment," Arteta said.
After winning just once in their previous five league games, Villa's second victory over Arsenal this season was a huge moment for Unai Emery.
Former Arsenal boss Emery delivered a tactical masterclass to frustrate his old club.
Emery's fourth-placed side moved three points clear of fifth placed Tottenham, who have a game in hand in the race to qualify for the Champions League via a top four finish.
"I'm very happy. We were fantastic. It was a very difficult match but we were ready to play," Emery said.
"We needed a high commitment in defence and then we had some transitions to get our chances. To beat Arsenal here is very difficult because they have been amazing."
Emery had repeatedly played down Villa's hopes of reaching the Champions League for the first time since 1982-83, but now he is ready to talk up their challenge.
"We played 33 games. We could be now contenders to qualify for the Champions League!" he said.
Asked if the result had an extra meaning after he was sacked less than two seasons into a troubled Arsenal reign in 2019, the Spaniard refused to gloat.
"Of course I had time here as a manager. But for me it is the same three points," Emery said.
