The Gunners' seven-match winning run in the Barclays Premier League was brought to an unceremonious end with a 2-1 defeat at relegation battlers QPR on Saturday.
Manager Arsene Wenger admitted his players lost duels all over the pitch, with Tottenham making the most of the opportunity to beat Swansea on Sunday and close back level on points in the battle for third place.
Walcott, who scored Arsenal's equaliser at Loftus Road, is in no doubt the Gunners will be ready to show their strength of character once more this weekend, where victory could all but end City's title hopes if Manchester United extend their lead to eight points in the day's early kick-off.
"I think that we can deal with pressure when it is thrown upon our shoulders," Walcott said on www.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."
Walcott added: "We are learning to grind out results now. The Everton game for example, saw us play very well for 20 minutes but after that it was all Everton. But we still won 1-0 and that is what we need to do more often.
"We have real character in the squad, a lot of leaders and captains, and that helps us."
Arsenal have not lost at home since being beaten 2-1 by Manchester United on January 22.
Walcott believes the Emirates Stadium can again prove "a fortress" on Sunday.
He added: "The fans expect us to win every game, and we expect to go out there, play our best and we feel we can win every game.
"The Emirates is starting to become a fortress, which is what we want it to be. That is with the help of the fans, they develop that.
"Away fans and players don't like to come to the Emirates, especially over the last few months. It helps us players, it is like having an extra man on the field."
Arsenal played a behind-closed-doors friendly on Wednesday afternoon against Birmingham.
Several of the first-team squad were involved in the 1-1 draw, including Johan Djourou, Alex Oxlade-Chamberlain, Yossi Benayoun, Marouane Chamakh, Gervinho and goalscorer Park Ju-young.
Although midfielder Jack Wilshere is continuing his recovery from an ankle problem, the England midfielder was never scheduled to feature in Sunday's action.