The Gunners kept pace with their north London rivals with a battling 1-0 victory at Sunderland on Saturday as Santi Cazorla netted the winner for Arsene Wenger’s men.
Arsenal are currently in fifth place in the Premier League table with 12 games left to play.
But Walcott says he and his team-mates are upbeat over their chances of securing Champions League football next season following back-to-back Premier League wins.
“We’re very confident [of finishing in the top four]. We can battle through any sort of situation,” Walcott told Arsenal’s website.
“The teams around us are winning as well, but we’ve just got to make sure we look after ourselves and try to win as often as we can.
“We’ll see where we are at the end of the season but we’ve got to show the belief we did at Sunderland. I felt there were a lot of winners in that dressing room and the boys were fantastic.”
Walcott was thrilled with Arsenal’s win at the Stadium of Light and is looking forward enjoying a free week ahead of a home tie with Birmingham in the FA Cup on Saturday.
“It was an important win,” he added. “The three points have us on a high and we’ve got a nice week now without any midweek game.
“A lot of players are back from international duty and need a bit of a break. Some may be rested for the FA Cup game, but that’s just as important as we want to go far in that competition. If we lost [at Sunderland], we would have been dwelling on it for so long, so I’m glad we didn’t.”
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