The Emirates Stadium outfit currently lie in fifth place, just four points behind fierce north London rivals Tottenham, and have picked up 10 points from a possible 12 in their last four league games.
"We're very confident [of finishing in the top four]," Walcott told the club's official website. "We can battle through any sort of situation."
|7/2||Theo Walcott is 7/2 with Paddy Power to score the first goal in Arsenal v Blackburn
Arsenal ground out an invaluable 1-0 win away at Sunderland on Saturday and Walcott believes that the confidence gained from the victory, plus the chance to rest players in the FA Cup against Blackburn, can propel the Gunners towards Champions League qualification.
"It was an important win; the three points have us on a high and we've got a nice week now without any midweek game," the 23-year-old continued.
"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.
"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."