Arsène Wenger has praised his players' response to a "difficult" week, after Santi Cazorla's late winner moved Arsenal to within a point of Tottenham Hotspur and the Premier League's coveted top four.

The Spaniard's goal lifted the gloom after successive home defeats to Blackburn Rovers and Bayern Munich had seen Arsenal eliminated from the FA Cup and effectively out of the Champions League. Wenger's side were still nervous for long periods against Villa, who have dropped back into the bottom three despite a spirited display, before prevailing late on.

"The result was vital today," Wenger said. "We absolutely had to win this game. We couldn't afford to drop points for two reasons: we're in a catch-up situation in the Premier League, and we've come out of two massive disappointments. But we were focused, united, a bit nervous … we played a bit with the handbrake on in some situations and the second goal didn't come until the end.

"But we were also strong because, when Villa came back to 1-1, we found the resources to win the game. I'm proud of the attitude of the team. We'd lost against Blackburn and Bayern here, at home, and when people come to the Emirates Stadium they should not be going away with wins. Personally, you do your job and focus.

"I've not been 30 years in this job at the top level to be destroyed by people saying I don't know what I'm doing. I would have stopped doing this a long time ago if that was the case. But we have responsibilities and have to stand up and get the team ready to fight. We went through some difficult days this week and responded in a united way."

Tottenham do not play until Monday, at West Ham, but host Arsenal next Sunday in the north London derby. "We cannot drop points," Wenger said of that fixture. "I've said that many times since we lost the Chelsea game [in January]. That's what is in our mind, no matter where we go and who we play. But the key for us will be our consistency. A draw today would have been a very, very bad result."