Saturday's shock FA Cup exit to Blackburn was compounded by a Champions League last-16 humbling at the hands of Bayern Munich on Tuesday night.
Arsenal face the unenviable task of attempting to overcome a 3-1 home defeat in Germany, with failure to do so virtually ensuring they would end an eighth successive season without a trophy.
Gunners boss Arsene Wenger has come under mounting criticism as a result and Walcott admits his team are in need of a morale-boosting win when they return to Premier League action against Villa.
"We've got the best man in the job to get our heads back to where they should be," the forward said. "I've played a lot of games in the Champions League and I know how things go.
"We need to react in a positive way s traight away. We can't be down in the dumps in training. Everybody needs to be alive and alert, recover well.
"We've got a good run in the Premier League - we can't forget that.
"We've had some good points, very important points, so we've just got to start believing again. I think that's one of the main things - believe in how good we are, because we didn't show it against Bayern."
Arsenal have just one win to their name in 2013 and are in a straight fight for fourth spot, having never previously failed to qualify for the Champions League under Wenger.
"If you are a top team, and with the saga of not winning anything for such a long time, it's always disappointing if that happens," Walcott said.
"But I don't want to focus on the negativity about that. I just want to focus on the positive side of the team, because I know how good those guys are, and get to where we should be."
One of the biggest recent issues has been Arsenal's inability to hit the ground running, with early goals too often putting them on the back foot.
"It's happening most weeks," Walcott said. "We didn't really have a slow start (against Bayern). It was just sloppy goals - goals that could have been avoidable, I felt.
"Bayern, we knew how strong they were going to be... they're very well organised, they did their job, they took their chances which is the most important thing.
"We had a few but didn't manage to take it. In the Champions League you need to take limited opportunities, but, like I say... got to take the positives out of the second half. There's a lot we can learn from that, learn from Bayern as well because we want to be like that.
"They're not fazed by anything. Like I say, they did a job."