The Gunners face Manchester City this weekend.
"I think that we can deal with pressure when it is thrown upon our shoulders," Walcott said on Arsenal.com.
"The manager always takes it on his back, but as players we can cope with that now because we had that tough period.
"We had a lot of injuries, things weren't going our way and Tottenham were 10 points ahead, but we dealt with that, we continued playing our football and completely turned it around.
"When people play at their full potential it makes the job so much easier. We need to learn to do this more often."